That's what I was going for. Seeing if it was the furnace or the thermostat.
Now that you've narrowed it to the furnace, you can concentrate on that.
Since you're hearing a click it's getting power to the time delay relay. I assume that's what you hear clicking. But the blower motor isn't running, right?
If you can access the blower motor, I'd hook 12 volts to it directly and see if it runs. If it does, then it leads to the relay/control board.
Salem 29RKSS Pushing a 2500 Mega-Cab CTD!
Gotta go campin!