New SATA II 500 Gig drives fail S.M.A.R.T. testing with Seatools for Windows but pass Sea Tools for D

Check if you get the same SMART errors when the drives are in a different system.

It's possible you got the drives from a bad batch, or maybe you didn't get new drives, but rather repaired 2nd hand drives. Another issue could be that your PC gets too hot inside, that could also heat up the drives too much which would eventually SMART to trigger it's threshold.

It could be that motherboard with its SATA controller is bad itself thus whatever drive you connect to it all fail to pass SMART tests.
Best of all to connect this failing drive to another system and run there SMART check from Boot CD. This will be most correct test as running SMART in Windows is not quite proper approach. When disk is used by Windows you cannot get to all sectors during this check.

In addition you can try to update MB bios if drives work correctly on other system.

Hi, Thank you so much everyone. I now know of some more things I can try. I did not know the SMART testing in Windows is not the same as the DOS testing. In DOS everything is fine including the temperature which is 22 for the drive. My CPU and motherboard temps are 25 and 24 so that is good. I also tried several  different SATA cables in case that had anything to do with it. I did see on the ASUS site that there were a whole bunch of BIOS revisions so I think I will do that first if this drive works in another system. You may be right about the drives not being new. The company I bought the motherboard from has gone under. I had the very same board a few months ago and it was bad. I hope that wasn't part of a bad batch either but one thing at a time. Thanks again. I will be back soon.

One would hope Seagate tier-two or tier-three support would be very interested in, and hopefully able to explain, the difference in result between their DOS and Windows diagnostics of the same drive in the same box.   The drive diagnostics SHOULD be the best test indicator.

S.M.A.R.T. is not perfect, but it "helps" to indicate problems (think idiot light on the dashboard) not all problems are caught by it.  Manufacturers will often have the threshold of some smart monitored datasets at "0" zero, which means that current/worst value for that setting will never exceed threshold, never raise the red flag as far as smart is concerned.  
Here's an interesting thread questioning why a smart tool reports ok but HDTune reports a different result  https://www.experts-exchange.com/questions/26407063/differences-between-HDD-Sentinel-and-S-M-A-R-T-readings.html?cid=1573&anchorAnswerId=33456801#a33456801

ASUS?  Excellent!  All their motherboards include chips for monitoring all things like temperatures, fan rpms, voltages so you can use ASUS PCProbe II and end-users can be alerted to problems.  Speedfan is another monitoring app, as is http://cpuid.com HWMonitor (free or Pro $)

Thank you for the valuable information and sorry not to get back sooner. I have in the meantime done many things, one of which is to apply the latest BIOS to the mainboard. No change in anything due to that intervention. I did mount 2 of the 3 drives onto 2 different computers each - one was an older Athlon Opteron system with an  ASUS board that is about 3 years old and another old HP system with a proprietary board - I didn't even bother to identify the chipsets when after running test in DOS and Windows the Seagate tests all passed showing the same results in both computers. At that point I decided that because I needed to get the computer back and running without any worries, I decided to mount the sytem onto a new board with the same chipset so that I would not have to reinstall the system, just update drivers. But, I had a sneaky suspicion all along that it has something to do with the board or the SATA controllers ( Nvidia Chipset G Force 7025/nforce 630a Rev.3 for the southbridge ) somehow being either damaged, incompatible or not recognized somehow by the Seagate Windows program. Well, it turns out that after successfuly migrating the XP system to the new ASROCK board, and being able to run the Windows tests on it that I get the same results as before from the Seagate Windows and Dos testing. Still all the SMARTS show up as Failed with different test codes for each drive but all pass the SMART with DOS. Both motherboards indicate that SMART monitoring is enabled and has not been tripped. I am no longer worried that something is wrong with the boards, either of them. I think it is perhaps not even a problem with the drives being defective in any way but rather that somehow the Nvidia Chipset might not be recognized by the Seagate for Windows properly. I will contact Seagate about this as soon as I can. The trouble was contacting them during the hours I had available - like this weekend but of course they are closed weekends and as I was always so busy when their tech support was available I did not get around to calling them during the week either.. Another weird thing happened after remounting the original drive that I had cloned onto 2 other drives, was that when I booted it up onto the new motherboard not initially but after the first boot and I had to install some drivers etc. well at that point it went through a disk check and found some errors on the disk with security descriptors and other attributes that were damaged but that went by so fast i could not record it. It all started out initially because the computer would not boot up and I had this blinking white cursor and in the computer's event viewer there were references to "Disk" I got that system to boot up finally by restoring a snapshot in the registry using my Bart Disk to access System Volume Information files and get the ones I needed from the config folder. That is why I downloaded and ran the Seatools for Windows to beging with. I have always tested the drives with both programs.  I also ran PIRIFORM's Speccy test and HD Tune ( which I forgot to tell you about) and SMART was not showing as tripped on either of them. I suppose more experienced technicians would know when to call it quits and that the one result was outweighed by the other results. But I do not have that skill yet to know what is probably not valid or valuable information and if everything had been working well I might not have gotten so worried. I am hoping I can just forward all this stuff I am writing right to Seagate somehow - I guess I will get busy cutting and pasting. Thanks again everyone and I will try to get back sooner than later. If anyone has helpful comments in the meantime I would appreciate it. Thanks oh_canada techguy for the links - awesome help I am getting everytime I am stumped.

SMART is a couple of parameters with thresholds that get recorded directly by the HD. If a threshold has been tripped then it is recorded and the disk will pass that on to the mainboard etc. This means that if you move the disk to another PC it'll still have that "failed" flag set, and if the BIOS has SMART enabled it must then report to that that the DISK is failing SMART and should be replaced asap. Normally this happens at bootup. If you are using a RAID controller, then the controller has to check the SMART status of the HD and pass it on to you, 3rd party tools won't have direct access to the individual Disks on the RAID controller, so that is probably the reason your seatools are giving erratic output. There should be a management utility for your controller that may show you the SMART status of your disks.

The autocheck chkdsk results should be logged in your Event Log.  Manual run chkdsk are not but the automatic ones are.

Wow, this stuff is blowing me away. All I wanted to do was to build a little computer to run Quick Books and  a Point of Sale program that was inexpensive because the company does not have a lot of resources right now but anyhow you live and you learn. Actually, it is very interesting and at the same time disturbing to know that makers of boards can screw up so badly. You either have a RAID or you don't and so  you would think both modes would be checked. Mine is not a RAID system, just a single drive in IDE mode. I have not installed the RAID drives for Windows as I saw no need for it. I will have to re-read all this latest stuff to make some sense to me. I am learning but you guys know all these neat things about stuff that when it happens to you you know what to do. I do a review on a mainboard before I buy it and if I don't find anything bad about it I figure it is OK.  Maybe I should find out firstly how to select a worry free mainboard. Also, maybe I should scrap the whole SATA drive install, remove it, disable it, install an IDE drive - Speed is not an issue - I don't think a few seconds here or there are going to matter for the applications use.  I will also write ASUS about my problem - you won't hear from me for a day as I have to work out of town all day and won't be back again in time to call Seagate so thanks you people a whole lot for your expertise and you will hear from me tomorrow.

I think this board has bad SATA controllers. I did not have any other brand of disk to test with it but all tests are fine in DOS on this board, but not in WIndows. The disks are fine in other computers. I ended up getting a new board with an Intel Chipset and all is well. I have read other posts on Google searches about bad SATA controllers causing similar problems so I am not going to spend more time on this. It is hard to know when you are new at something how much time to allocate to a problem. I did disable the SATA in the BIOS and installed an IDE drive on this new board and sold it to a senior who wanted a board to surf the net and do online banking. It more than fits the bill for this purpose. He is absolutely thrilled with the performance compared to what he had before so everyone is happy and I did not lose out any money. Thank you everyone for your comments and suggestions and comments.