Yep, it's better to troubleshoot first. It means you strip your computer to BARE essentials and try to boot. By stripping I mean remove every component from your motherboard, reapply heat compound to cpu, reseat ram, replug every cable etc.
One hdd, cpu, ram, onboard video if you have one - will it boot? If yes, try adding more hardware untill it crashes, one by one.
If you can post and boot to a linux live-cd, run memtest x86 to test your ram. The test must run through flawlessly if you have even one error your ram or motherboard is either bad or incompatible. Check that your ram is approved for the mobo/cpu combo.
If no boot, try swapping harddrive, install OS there and try if it boots. If yes, you probably have a bad hdd in your hands.
If still no boot then start looking for cpu, motherboard or power supply problems. Try to swap each component if you can - if you can't then you at least know where to start not to spend money on parts you don't need.
If your cpu is bad, your computer most likely just refuses to post totally. Just a reminder.