Hi there,
It sounds kind of odd that the power button does nothing at all, so make sure that everything is plugged in correctly, and I'd recommend trying the power button on the motherboard (or shorting the power pins) to make sure that it isn't an issue with the case button.
If that doesn't fix the issue, I would recommend clearing the CMOS on the PC. To do this, unplug the PC, take out the CMOS battery (the CR2032 watch style battery on the motherboard), wait 5-10 minutes, reinstall the battery, and try to turn the PC back on.
Alternatively, if your motherboard has a dual BIOS option (like a small switch on the motherboard that lets you choose between BIOS A / B), you can try switching to the different BIOS image and booting...