Check to see if the fan(s) in your computer are running or if any lights come on in the computer when you try to turn it on. If no, then it's most likely a bad power supply, although I am a bit confused about how your monitor is drawing power.
Start by jiggling the power cord. If that doesn't work then I wouls suspect that the power supply is the culprit.
The power supply is a metal box in the back of a tower computer where the power cord enters the computer. It contains a transformer and power distribution curcuits as well as a cooling fan.
It is possible to test the P.S. to determine if it is carrying current. I called a computer repair shop and they conduct a diagnostic test on all computer hardware for $40 USD. That would tell you if it was the P.S. or something else.
A new P.S. costs between $20 and $40 USD. Remove the P.S., carefully unplug all cords that go from teh P.S. to your computer's components and take it with you to a coputer shop. Ask for EXACTLY the same one as there are many different configurations and they won't all work on your machine.
Ryan
June 2004