A quick way to check to see if your power button is broken is to unplug the lead from the motherboard, and plug the reset button to the power button pins instead. If the reset button works, then you indeed have a power switch problem.
Depending on what case you have, finding a replacement power button could be tricky. Most places that sell components usually sell generic replacement switches. They may or may not fit your case. You can always check with the case manufacturer. If it is a major brand, many times they will ship a free replacement.