The two most common sources of problems/instabilities. Memory and the Power-Supply.
Check the rails on the PSU with a multi-meter using the green -> ground paperclip trick.
Boot up the machine with only the CPU, Mobo, PSU, Memory. What kind of beeps do you get? (if any?)
If you don't get a beep or any startup, swap out components in this order: Memory, PSU, Mobo, CPU
If you do get a beep, see what the beep translates to.
Usually your CPU isn't the picky one, it's the mobo.