Random BSODs 9 different codes

This is the strangest thing I've ever seen. For background, I'm a tech guy and ran an IT department for years.

I lived in New Mexico and took a job across the country to Virginia. My computer (very old, but trusty) was running just fine. I put it in a box with an insane about of packaging and shipping it along with most of my belongings to a relative's house on the east coast. Problems came up during my move and it wound up staying in that box for about a year until recently when I've been able to resume normal daily things.

After connecting the machine and starting it up with all the same hardware connected (even on the same desk), it seems to work fine until the STOP errors started happening, about an hour after the first boot. The STOP errors keep coming, different errors all the time, sometimes 1 minute after boot, sometimes 15 minutes, but never more than 30 minutes. I've tried un-installing and reinstalling just about every device driver, but it hasn't let up.

I'm inclined to nuke the install and start from scratch, but being the IT guy I am, I kinda want to know WTH is going on.

The nine different STOP errors so far:
7E
0A
DA
1E
24
3B
119
3D
1A

I'm starting to think it's a hardware fault and I'm going to start by running an extended RAM test (basic passed earlier) while anyone looks at the logs, I'll reply in this thread with the results.

When the attached diagnostic was run, the graphics driver was current un-installed still, but the STOP errors kept coming. Appreciate the input!

Well... I'm a little disappointed that I didn't get a single reply.

That being said...

I put my machine through some rigorous individual testing trying to figure out what exactly was causing the STOP errors.

Extended RAM tests yielded no errors.
CPU stress test yielded no stability problems.
Graphics stress test yielded no problems.
I even ran a sector scan on the drives to verify there was no read errors, and there was not problems.

I did all that from bootable USB drives. When I was done I decided to boot back into Windows to dive into the STOP codes a little more before going nuclear... and then it never happened. No STOP errors - they were just gone after all the testing. Makes me really wonder about Gremlins.

In reality, I wonder if there was some kind of... "staleness" to the hardware that burned off after all the stress tests? I know, it sounds ridiculous and if someone suggested it to me I'd call it tomfoolery - but what else is left as an explanation for a problem that both mysteriously appeared and then disappeared?