One thing to try is Memtest Memtest86+ - Advanced Memory Diagnostic Tool
Download and burn the iso to CD (Precompiled Bootable ISO), or try the NEW file for USB stick. Boot the computer with either media loaded. It runs without Windows.
Run it for at least 3 passes (overnight - takes a while).
You should get no errors.
Those errors, if not RAM, could be caused by a failing power supply. Check all the power connections carefully.
Could you find a power supply to borrow to test to see if this is the cause?