Did I fry my Furnace Control Board? (C -> G rewire attempt)
How thermostat signaling works (and how to test manually)
First, a little background about the thermostat control: It's dumb. Really dumb. The signaling is done by simply shorting wires together. The R wire is shorted to W to call for heat, or R shorted to Y to call for cooling, or R shorted to G to call for fan. Stuff, like digital thermostats, can be powered between the R and C wires.
You can test the furnace controls without the thermostat. Simply short the R and W (or R and Y) wires together and verify that heating (or cooling) begins.
This can be tested right at the furnace control board too, avoiding all doubt about the thermostat wiring. Note that the control board is often found in the blower cabinet and you're going to have to defeat a safety switch to perform testing there. It's your responsibility to ensure this is done safely -- you don't want clothing, long hair, or other things being sucked into the blower while working here. There also may be high voltage terminals exposed, so be careful about what you touch. Bypass the safety switch with one hand and, with one or two other hands, touch a jumper wire (a paperclip will do) between the R/W or R/Y terminals on the control.
What probably went wrong
To call for fan the thermostat will short R to G. But you had C on the G terminal, so the thermostat shorted R to C. That's a dead short across the 24v transformer in the furnace. Either the switch in the thermostat will have failed, or something in the furnace will have failed. Control boards often have a small fuse, about 2 amps or so, to protect the 24v side of things. It could be that the fuse has been blown.
How to diagnose further
If the manual tests shorting R/W and R/Y didn't cause the furnace to operate then get a multimeter and set it for AC volts. Turn on all power to the furnace and safely bypass the blower door safety switch if appropriate. Confirm (measure) that full AC mains voltage is supplied to the controller. If it is, then measure voltage between R and C terminals. You should find something in the neighborhood of 24-32 volts. If not... we'll have to dig deeper by examining the control board for a fuse, testing continuity of the fuse, testing the output voltage of the transformer upstream of the fuse, etc.