Chris:
Could be the power supply. First, test the electrical outlet by plugging a lamp into the socket.
Power supplies have fuses that are designed to blow if your system is demanding too much power or if your home experiences a power surge. Don't replace the power supply unless you know what you are doing. If you do replace it, be sure to unplug the computer, first.
If replacing the power supply does not fix the problem, you may have to replace the motherboard. Check the motherboard for any signs of damage (for example, discolored or cracked chipsets).
Do you hear any sound at all or see any other signs of "life" when you press the power switch?
