|"Is it my ram memory failed or did my motherboard fail?"|
Without trying a known good memory stick, it is undetermined. Then again, a bad mainboard can damage memory. The question is more of how lucky do you feel?
You can purchase new memory and try.
Or you can spend that money to purchase a mainboard assembly (CPU & RAM included).
One thing that was not addressed is the power supply. If that is bad or has a low output, all sorts of odd things can happen, including damage to the chips. Check that with a good power supply tester, or have it tested.