I'm gonna guess here that not all of it is wired up properly....from looking at your diagram there anyway lol.
Umm....from looking at your diagram...Are you actually trying to push the wall AC straight into the 7805?
The 7805 only regulates DC current, not AC. You need an 8-12volt (output) transformer. This is probably why nothing is working, and why the 7805 is heating up so much.
It takes alotta abuse to cook a 7805, so it may still be good...
Also, do you have the capacitors on each side of the 7805? They're kinda important too lol. As is having a resistor hooked in series with the LED to keep the LED from burning out. I'm guessing you'd probably need somewhere round a 160-180 ohm resistor in there to keep future LEDs from burning out.