I know this sounds strange, but...
Try unplugging it for 15-30 seconds, plug it back in, and then try the power.
Had a similar issue with my last PC and that solved it every time.
If the green light in back is on, that suggests that your power supply is working, so it's probably just not getting the power-on signal from the switch, which is entirely possible after a power outage. Disconnecting it from external power should reset things and get the power button working again.