Obvious places to start is checking that the power cable is in all the way, switched on at the wall socket and that the fuse hasn't blown in the plug/extension lead. If they're all ok it could be a dirty contact or a faulty switch on the power button, a loose connection attached to the switch or worst case scenario your main PSU (power supply unit) has died. It's not the end of the world if it has, swap out the old one and invest in a quieter replacement from QuietPC