Won't start, flickering lights

I parked my car and when I tried to restart it 5 mintues later, all the dash lights starting flashing on and off and the ignition just clicked on and off. Now headlights, accessories, etc. nothing is getting power. Checked the battery it registers 12.7 volts, cleaned the battery connections. Nothing.

I'm willing to bet you have a blown fusible link or a blown fuse. Check under your hood for the power distribution center and look for an 80 amp MAIN fuse, if that's blown that could cause your problems your having.

CLean the battery connectors again..at both ends of cable. Then..what age is battery? This also sounds like a shorted cell. This happens regularly for 5-6 year old batteres and the result largely mimics corroded connectors. Testing 12v at battery with no load is meaningless. Test voltage on battery cable connectors with a load...and even when starting. Should not go below 10V.
Again, this is typical and classic "broken" battery supply.