The BIOS string you have, searching on Google, seems to indicate an Emachines version of a D845GVSR motherboard (.44t.). See the following website go for supported processors for the Intel version of the D845GVSR:
There it looks like processor compatibility is dependent on certain revisions of the board and installed BIOS version.
Understand that the BIOS you use should come from the "manufacturer", here Emachines. They might have specific settings to enable their motherboard. They also might support the same processors, or not. I suggest searching the Internet for specific information for the Emachines D845GVSR.
Here's a link to the Intel® Desktop Board D845GVSR Technical Product Specification:
Here's a web location for manuals, Support and Troubleshooting:
With what you have going , i would recommend going back to the original configuration on both systems.
Disconnect the HDD or just boot into the BIOS set-up screen and let them sit for ~ 1 hr.
If the crash or reboot from BIOS set-up, you have ruled out the HDD and the OS and have a very strong indication of a hardware issue.
If they are stable, i would look for a DOS based diagnostic stress test such as memtest86 http://memtest86.com/ to check the hardware under load.
You can create a bootable USB stick or CD and run with out needing the OS.
If that checks out stable your OK, you down to HDD \ OS issue,
OS corruption (virus, etc) are common.
HDD's are the highest wearing \ failing item in a computer.
Since the Goodwill system (I get a lot of chassis from GW. I usually trash the old MB and start with something much newer) is a don't care on the HDD contents, you can try a reload the OS from CD (hopefully you have some window install CD source)
Many HDD manufactures post diag packages for the HDD's as well that can check to see if the HDD is about toasted.