99% of the time these issues are caused by RAM. There's a program called memtest you need to run... which is an issue if you can't get your computer on. Other problem is the PSU, though CM PSU's tend to be pretty decent (not the best for their low cost they run well).
You need to put the RAM into another computer and run memtest through it. You just need to dl a memtest iso image and burn it to a cd, and boot off it. Let it run until it finishes atleast 1 'pass' - it'll be obvious if there are RAM issues. RAM issues can be caused my your motherboard, but it's highly unlikely.
Edit:
You say it won't turn on. You press the power button - exactly what happens? System beep? Fans speed up? Nothing at all? It's important.