Assuming the system is not passing its power-on-self-test (POST), many components could potentially be to blame.
Firstly, try re-seating the RAM, as this is a very common cause of a failed boot. If this doesn't fix it, it would be wise to try using a known good GPU/graphics card, as lack of video output from a dead GPU (or bad monitor/display, for that matter) can very easily be mistaken for a failed boot attempt, especially if the motherboard lacks some sort of status display or beeper to indicate errors. If nothing else appears to be the issue after extensive troubleshooting, the power supply, expansion cards, CPU (either failing in some way, requires a BIOS update to properly function, or is simply incompatible with the motherboard in question), and/or the motherboard itself could even be to blame.
Hope this helps!