Try Bill's suggestion of reinstalling the Operating System first, then see if things are stable.
Make sure to have all the hardware [drives, adapters, etc] as they were when you first pulled the boxes apart and turned it on the very first time. That's the way the restore utility will attempt to do things.
If the GPF persists, try a "Clean Install" by using a stand alone version of the Operating System [Windows]. This will require you to get all the needed drivers for your stuff [Audio, MODEM, Video, etc.].
Best if you perform a full format prior to anything. use the "Unconditional" switch, which is /u. The syntax at the command prompt [DOS prompt, AKA the "C" prompt] would be:
FORMAT C: /U
Also verify the disk has been setup for FAT32 by running FDISK at the command prompt. If not setup for FAT32, this might cause Kernal32 errors.
Some applications that run in real mode have conflicts with the FAT 32, so this would cause the error also. These would be older apps, like ones written before 1997. Ones that keep the file names to the 8.3 structure would be suspects.
Another sort of likely suspect would be DRAM failure. It may have been masked prior to the reinstallation, due to what ever way the Operating System decided to allocate Kernals.
Try to get the fault to occur in a predictable matter. When you get the fault, close your applications, restart windows, then try to make it happen again.
See where the locations [shown in hexadecimals] are listed each time. Random locations would be software, but not always.
Is this coming up as a software level fault? [the windows dialog box]. Is this shown as Invalid Page Fault or GPF [General Protection Fault]?
Is there a corresponding Hardware fault screen [AKA "The Blue Screen Of Death"]?
These can point to hardware problems [could be as simple as a buggy driver, to a failing adapter] and may warn of impending Power Supply Disaster!
Let me / us know what's up!