HP Laptop Win 10 boots fine through startup and clears HP and login pages but then freezes (every time) midway through icons loading on home page.

Isolate hardware or software.

Get the HP Hardware diagnostics for your model. You should be able to get them (disk for sure) on a bootable USB key. Start with the USB Key and test all hardware including the hard drive.

Then if hardware passes, do a Windows 10 Repair Install and Keep Everything.

https://www.microsoft.com/en-us/software-download/windows10

Windows 10 is running, so click on the Download button (not Upgrade Button, select Save.
Create a USB Windows Installation key and then run Setup on the USB Key.
This will launch the Repair and proceed normally.

Hold the Shift key during boot and start it in Safe Mode to see if it boots.  If it still freezes, then your hard disk is likely failing.  Replace it.  If it starts fine, then you have a driver issue.

i would start by testing ram and disk with the proper diags, to be sure about the basics
i use ubcd for this :
Hardware diagnostic CD    UBCD
---------------------------------------------------
go to the download page, scroll down to the mirror section, and  click on a mirror to start the download
Download the UBCD and make the cd   <<==on a WORKING PC, and boot the problem PC from it
Here 2 links, one to the general site, and a direct link to the download

since the downloaded file is an ISO file, eg ubcd527.iso - so you need to use an ISO burning tool
if you don't have that software, install cdburnerXP : http://cdburnerxp.se/

If you want also the Ram tested - run memtest86+ at least 1 full pass,  - you should have NO errors!
direct download :  http://www.memtest.org/
 
For disk Diagnostics run the disk diag for your disk brand (eg seagate diag for seagate drive)  from the HDD section -  long or advanced diag !  (runs at least for30 minutes)

http://www.ultimatebootcd.com/      

**  you can make a bootable cd - or bootable usb stick
*** note *** for SSD drives  use the tool from the manufacturer, like intel 's toolbox :
https://downloadcenter.intel.com/download/18455/Intel-Solid-State-Drive-Toolbox

for completeness -here's how i handle disk problems : http://www.experts-exchange.com/Storage/Hard_Drives/A_3000-The-bad-hard-disk-problem.html

==>>****in order to be able to  boot from CD or usb - you may have to disable secure boot in the bios

Apparently it is the HD...I have an error message as the SHORT DST check failed with a failure I.D. of MCROG1-8P99GF-XD7URG-6OVLO3
Product I.D. 1NT81UA#ABA      I have a feeling the O's and 0's maybe messed up as their are no 0's 'crossed to indicate a zero.
Extremely aggravating as inputting the computer's serial # into their search field turns up nothing, as does the product I.D.
I'm not giving  a hundred bucks to HP for them to tell me i have a bad HD on a 2-3 year old computer. Any ideas on whether or not it's definitely the HD and whether or not it's salvageable? I can always just pull the files off using safe mode. Thanks in advance. I still can't believe that this hard drive went south so quickly, but I guess it happens. Thanks for any additional help in advance.

have an error message as the SHORT DST check failed with a failure I.D. of MCROG1-8P99GF-XD7URG-6OVLO3

That is a hard drive error as first suggested here. The error pretty much confirms that.

3 years old ?  If the computer is otherwise OK, put the drive in a carrier, recover what you can, and get a new drive.  

You may wish to get a new, better and faster computer at this point

Something else that is really annoying me...after reading about these short DST checks, it says that the problems can be anything from  "Application or driver conflicts, virus issues, file corruptions due to incompatible applications, improper shutdowns, or update failures due to conflicts." REALLY? So problems that I used to be able to troubleshoot and correct now have to be resolved by replacing the hard drive every time? My specialty used to be fixing blue screens without ever having to replace hard drives...so you're telling me that now since windows can't fix the problems correctly (and hides the exact problems under the auspices of several bootup screens) that means a new HD is the only answer? If that's the case, I'm finally going to switch to a Mac.

There is nothing above that is a BSOD error (mini dump file) that I can see. I think the HD is a problem here.

The fact that error messages are no longer given every time a screen freezes (in Windows 10) and you are then forced to improperly shutdown your computer tells me that these problems are never really fixed. Especially when "improper shutdowns" are given as an actual cause for HD failure! What are you supposed to do when Ctrl/Alt/Del doesn't shut your Win 10 computer down? You're forced to shut it off manually!  Eventually these problems stack up somewhere in the HD, unfixed,and after enough of them accumulate...Oh sorry...it's your HD. That's total BS. When my Long DST Check results come back in 10 hrs. and it Passes, I'll let you all know. There is something very wrong with the way this OS works, as it takes the troubleshooting expertise out of it and replaces it with the 'appearance' of knowing how to fix the problem. But System Restore was totally unavailable from boot...and I updated it weekly! Also, diagnostics could do nothing either! I'm not giving up on this...I'll fix it myself if I have to replace a file at a time to do it.

On a properly operating computer with good hardware, you will not get these errors. We have lots of Windows 10 Pro machines. around.

If you are convinced the hardware is good, then try the Repair Install I suggested in the first response here.

what is this DST check you ran?  what diagnostic?  i know DFT, but notD ST
you can test some disk drives when connected on USB
if the disk is bad, your options are :
1- backup and install new disk
2- try to repair it with HDDRegenerator : http://www.dposoft.net/hdd.html      
*** it can be you need to do 2) first, in order to be able to backup