Is there physical damage to the power button itself? If so, you'll need to replace the front panel (or the entire case). If not, and you do feel a click when you press the button, then the problem is likely with the mainboard (the power button simply activates a relay on the board that turns the power on).
motherboard LED is flea Standby power. This DOES NOT MEAN that the power supply is ok only that 5W of +5vsb is working. Typical power supply does this by using a linear power supply in parallel to the switching power supply. CMOS battery could be dead however. I would remove power and all cords then remove battery and replace then see if it comes back on.