Need help with BSOD mainly at startup, ntkrnlpa.exe error.

No problem, Lee. Just let us know whenever you can.

Lee, the file you uploaded contain only files which are older than the first ones you sent. The one you uploaded, the latest dump file was 9-24,I believe. In the first dumps you uploaded, there were dumps in late November. Have you run some type of disk cleanup tool? most of them clean out error reports by default. Please make sure uour computer is configured for small memory dumps, Dump Files - Configure Windows to Create on BSOD

also, please run the BSOD posting instructions again. Try option 2 and press the 'grab all' button.
Blue Screen of Death (BSOD) Posting Instructions

This dump file had 3 dumps later than the original, however there was little new information I could get out of them because of the particular problem. The dumps were pretty much the same as the original ones.

Code:

CRITICAL_OBJECT_TERMINATION (f4)
A process or thread crucial to system operation has unexpectedly exited or been
terminated.
Several processes and threads are necessary for the operation of the
system; when they are terminated (for any reason), the system can no
longer function.
Arguments:
Arg1: 00000003, Process
Arg2: 87c07d40, Terminating object
Arg3: 87c07eac, Process image file name
Arg4: 82e60ec0, Explanatory message (ascii)

Do I understand correctly you ran checkdisk f/r and no errors were found and ran sfc /scannow and no integrity violations were forum?

I know you sais you ran Seatools, did you run the short and the long test? If not, please do so from a DOD bootable disk or USB flask drive. You will need to boot into the media you choose. These are the instructions SeaTools for DOS and Windows - How to Use

maybe it is just me, but I cannot believe it is anything other than a hard drive problem or possibly a virus. If this turns up nothing we will take a different course, but it will take time with the computer.

Lee some online scanners that I use. There may be more:

Kaspersky TDSSKiller:
Anti-rootkit utility TDSSKiller

ESET online scanner:
Free Virus Scan | Online Virus Scanner from ESET
Free Online Virus Scanner | ESET

Microsoft's Windows Defender Offline
Windows Defender Offline

I apologize if I am off base, but I have always said that a stop F4 was a storage problem. I just may be wrong. Here is something else you may try. Before doing anything, create a restore point, it may be your only way back. The tutorial of how to do it is in the link below. I would like you to run it for 24 hours of actual use, doing anything and everything you normally do. If there is anything that causes a BSOD Normally, do it a lot. The idea is to put stress on all Non-Microsoft drivers in hopes of causing the problematic one to cause a BSOD and catch it in the dump file. When you set it up, sort the drivers by provider. Select all drivers not provided by Microsoft. It will make the PC seem slow and sluggish, that is normal.

   Warning

Be sure to create a System Restore point before proceeding further System Restore Point - Create

Driver Verifier - Enable and Disable
Run Driver Verifier for 24 hours or the occurrence of the next crash, whichever is earlier.

   Information

What is Driver Verifier:
It puts stress on the drivers, and tries to make the faulty driver crash the computer. It is designed this way, to attempt to trap the offending driver.

What you will notice:
It will tend to make the computer rather slow and sluggish because the drivers are being stressed.

   Warning

Before enabling DV, make sure you have created a system restore point before enabling Driver Verifier. make a System Restore Point manually before enabling DV.

   Tip

• If you fail to get on the Desktop because of DV, Boot into Advanced Boot Options > Safe mode. Disable DV there. Now boot normally again, and try following the instruction of enabling DV again.
• If you cannot boot in Safe mode, do a System Restore to a point you made earlier.

Let us know the results, with the subsequent crash dumps, if any.

The Event Logs show BIG problems with SOPHOS.

I would recommend uninstalling all Sophos software, and using the company's removal tools.
How to uninstall the Sophos Control Center
How to remove Sophos Endpoint Security and Control from client computers

As a temporary measure, install MSE as your AV - Microsoft Security Essentials - Microsoft Windows

Thank you Noel, I guess I owe you again.