It's always a good idea to start your diagnostics at the lowest level and work up.
Disconnect all peripheral devices - hard disks, optical drives etc.
Ensure that the case speaker is connected correctly.
Connect monitor to onboard video.
The machine should boot as far as the BIOS screen and (with error messages, of course).
If it doesn't get that far, there should be beep codes.
If there are no beep codes, then it's failing to boot entirely - which would indicate one of the following:
Badly seated RAM
Badly Seated CPU
Failed CPU, or Motherboard, or incorrectly powered motherboard. A common mistake is failure to connect the additional 12 V line, if there is one.