It's probably a combination of factors, but it boils down to several things:
1). A disparate collection of old second hand hardware which may not have been handled in ideal ESD conditions.
2). Very low quality PSUs generating DC supply rails of questionable quality.
3). Flaky local mains supply, especially if you suffer brown outs, over voltage, frequent power cuts, mains transients (spikes), surges, etc.
I've bought dozens of second hand motherboards, CPUs, RAM, plus a few graphics cards, on eBay, but I'm very wary of second hand PSUs. A PSU is the most important part of a system and bad PSUs can kill motherboards.
I've measured local mains supplies on vacation as low as 55V AC and as high as 330V AC. Neither of them are good news for switched mode PSUs which typically bear a label showing 100V - 240V AC 50/60Hz. You can run PSUs outside these voltage limits, but go too far and it's "magic smoke" time. In the case of the 330V supply, all the light bulbs in the room had exploded. A faulty petrol generator with a broken speed governor was the cause.
Dare I say it but if you buy new equipment and an AC line conditioner + high quality UPS (if your mains is flaky), most of your problems should go away. It's a shame this will probably be impossible if your school does not have an infinite IT budget.
I'd suggest checking the RAM in each PC by booting up from a USB memory stick loaded with MemTest86.
https://www.memtest86.com/
This should help to determine if any DIMMs are faulty. If you get any failures in MemTest, repeat the test with one DIMM at a time, until you find the bad one(s). Discard any RAM that fails MemTest, or switch off XMP memory overclocking in the BIOS.