If you mainboard has 2 RAM modules, you could remove power from rrear of PSU, remove one RAM stick, and try operation with only one installed, and, if no improvement in stability, try the other RAM stick...
(Or, you could try an overnight run with a bootable memory tester such as Memtest86, etc...)
Naturally, a failing drive can also induce corruption that can cause crashes, blue screens, but, such a system would run a bootable Live CD image from USB just fine (Linux Mint, Hiren's Boot CD, etc)