Why are my hard drive and DVD drive not recognized?

Are the devices older?  Go into BIOS and set AHCI to Compatibility mode. Then start and try again.

There is no option to set AHCI to Compatibility mode.   The three choices are AHCI, ATA or Disabled.   There was a RAID card in this system when I got it.   Not sure if this makes any difference.

Could be then that the devices are not compatible with you System. Try USB DVD and Hard Drives and see if the work

It seems the HDD 0 and HDD 1 connections are not operating, so the devices plugged into them are not recognized.   Is there some way in Setup to check this?

You legacy arrangement which you say you can't do. Maybe update the BIOS and see

When I connect a DVD drive and a hard drive to HDD 0 and HDD 1 respectively, they do not show up in setup.

Attach your SSD to SATA 0,  Connect your Optical drives to HDD 0 and HDD 1 port and remove the RAID card, make sure RAID is disabled in BIOS  and select AHCI / ATA mode from BIOS and test.

SSD works fine connected to SATA 0, and a hard drive connected to SATA 1 is recognized and I want to use it as a backup drive, but the optical drives connected to HDD 0 and HDD 1 do not show up in device manager.   Is there some setting in the BIOS to allow HDD 0 and HDD 1 to work?   Perhaps they are disabled in the default setting, since there RAID card was installed originally?

Is there some way to test HDD 0 and HDD 1?

Use the Dell hard drive test application

it seems that you can have either SATA 0 and SATA 1 or HDD 0 - HDD 3 ports only in a software RAID mode without a RAID card.  

These are your options:

Please read this Article:
http://www.bbt.si/modules/uploader/uploads/s_product/file/57f3e3148e4eb_dell-precision-t5600_copy1.pdf

I just want to have the two optical drives as well as the SSD with Windows and a second hard drive working.   Please tell em how to do this.   I do not want to have a RAID setup.   It is too confusing.

If the current stuff does not work use USB devices

you could install a PCIe to sata controller  like this :  https://www.newegg.com/global/be/Product/ProductList.aspx?N=100007607%20600022631&IsNodeId=1&Submit=ENE

Download all selected drivers from below link and retest.
http://www.dell.com/support/home/us/en/04/product-support/product/precision-t5600/drivers
Update the BIOS to A15.

I have already updated the BIOS to A15.   I downloaded and installed the drivers, but the optical drives connected to the HDD slots still do not show up  in the BIOS.   What does show up is a yellow exclamation point for SAS controller.   Does this help?

How about setting the BIOS to factory default?  

I still have the PERC H310 card that was installed in the computer when I got it.   One of the connectors was connected to one HD.   There was no second HD installed.   Can this be used with only one HD instead of two as a means to connect one HD?   I guess I could set up RAID 0 or RAID 1 with the card and then reinstall Windows if I can get it working.   I do not know how to configure it to do this.   I currently have Windows installed on an SSD, so I suppose I could clone this to a newly set up RAID.   Please advise.

If the drives are compatible, you can set up RAID 1 on the machine

What does show up is a yellow exclamation point for SAS controller.   Does this help?

Download and run the free trial  of Driver Genius and let it to find driver for SAS controller,
http://drivergeniusprofessional.com/

Can this be used with only one HD instead of two as a means to connect one HD?

You have to try all possible combinations of Ports and modes,  because you can hardly find any information related to Attaching SSD and HDD with two optical drives at the same time to that Motherboard.

Regarding the mode of the drive controller, ATA is the equivalent of legacy. However, on your Dell I'm not sure how granular the BIOS is when it comes to configuring the storage controller. I'm assuming that the optical drives you want to connect have PATA (IDE) interfaces; if so, you may find that it's an all or none scenario with the BIOS in which every port is either ATA in ATA mode or the PATA ports are disabled in AHCI mode, leaving only the SATA ones active.

The simplest method of achieving what you want may be to set the storage controller to ATA mode, so that your optical drives will be seen by the system regardless of whether they are SATA or PATA, and re-install the RAID controller for the remaining SATA drives. Configure the RAID controller as JBOD if you have the option to do so, otherwise you'll have to set up a RAID1 array for the remaining disk(s). You might be able to run a single drive on the controller, but even if you can you'll be forever plagued with error messages about degraded arrays and missing drives.

The optical drives are SATA.   I have been unable to find a driver for the PERC H310 card.   There is none on the Dell website.   If I could find that, I might be able to use the card.   If all else fails I will just forget about it and reinstall the SSD with Windows and connect one of the optical drives to the other SATA connector on the motherboard.   It seems a pity to be unable to use the HDD connectors.

what about my suggestion to install a controller card?

Now everybody is happy

Me too,  thanks for your feedback.