While installing shelves, I put a screw right through a wire in the wall. The breaker didn't even budge. Didn't know or have any problems until the next morning when I tried to open my garage door. It made a noise but didn't open and the furnace powered down as I pressed the button. From this moment on, no heat, just the blower working.

I had the wiring fixed. The furnace would short cycle, no more than 10-15 seconds. Then I opened up my thermostat and put it back together, just trying to reset it (if that is even a thing). Now, the furnace just clicks repeatedly when I turn it on. No blower, no nothing. And the garage lights flicker off and on as the clicks happen.

I tried new 3 amp fuses. Problem persists.

Any ideas what is going on?