Most likely OS issue:
I would guess the most likely problem, even though you gave no symptoms, is that there is something wrong with the OS or software. I would run a Linux live cd for a while or do a fresh install, and see if you have issues.
More Likely RAM:
What makes you think it is failing? I would guess RAM or the motherboard first. I recommend memtest to check the ram.
If you are having CPU problems, is it related to heat?
Time vs. Hardware Cost:
Is this stuff worth the time? If it is expensive, maybe it is still under warranty? If it was expensive, can you get something more powerful for cheap?
Lastly, what are these weird symptoms?