A couple of possiblities:
1. Have you tested the machine with another power supply? The LED works on one of several voltages the supply is supposed to provide, but I'm not sure it reflects whether all required voltages are present.
Recently, I repaired a friend's HP desktop that showed the same symptoms; the LED on the motherboard was lit, but it would not start. I connected another supply to it, and it started right away. Replacing the supply fixed the problem.
2. The front panel start button is a single closure that momentarily shorts a logic pin to ground. If the switch has failed, the machine won't start. You can test this by shorting across the two connectors on the switch, or between the two pins on the motherboard where it connects.
Good luck.
