Without much info about exactly what happens when you turn on the system, system parts list/specs, it could be anything form the monitor being off to a dead power supply to the power outlet being bad, motherboard issue, etc...
What exactly happens when you turn on the power? Does the system seem to turn on, fans spin, beeps, lights, etc.. or totally dead? Did you check anything already like re-seating RAM, resetting BIOS, etc..