I unpluged p.c. during a storm and when I pluged it back the power button would not respond? And the power indicator light on the back of p.c. is now blinking? Slowly when unpluged, and faster when I plug in the power cord??

When you plugged the PC back into the wall, there may have been a build up of electricity between your house and the powerlines outside..
If that's the case and you pugged in the PC before any other devices into the wall, it may have damaged your power supply and you may need to get a new one...

Before exploring that option, I suggest opening the case and clearing your bios/cmos
Check your computers manual for instructions on how to do this.
The computer not turning on anymore after plugging it it back in
Just may be a coincidence and not have anything to do with the storm at all.

It may also be possible that your computer will not turn on if your bios battery is no longer holding a charge and may have to buy a new one...
You can get a bios battery almost anywhere for under 10 dollars