The cooling test sequence for this board, says to jumper Y & G to R. Make sure the fan comes on, and spins up to the proper speed. Then remove the jumpers, and check the fan off delay.
If the blower does not come on, verify that the COOL terminal is energized. Use a voltmeter between COOL and neutral, and verify 120 volts (with jumpers in place).
If the COOL terminal is energized, check the motor and verify all speeds are working properly.
If the COOL terminal is not energized, the board my be bad.
According to the schematic you've provided, you have a multispeed blower (which is quite common). The speed at which the motor runs, is determined by which wire is energized. Energizing the red wire; for example, will run the motor at low speed. Energizing the black wire, runs the motor at high speed.
Before you disconnected the board, one of the motor wires was connected to the HEAT terminal on the board, and one was connected to the COOL terminal. Looking at the ladder diagram, it looks like the blue (MED) wire was connected to the HEAT terminal, and the black (HI) wire is connected to the COOL terminal.
If you've run the tests described above, and found that the COOL terminal is energized when the jumpers are in place. You can try connecting a different speed wire to the COOL terminal. If the motor spins up with the other wire connected, it means that the original speed is dead or something's wrong between the board and the motor.
It looks like the LO speed red wire is attached to the M1 terminal on the board. I'd swap that to the COOL terminal (just temporarily for the test), and see if the motor spins up when the jumpers are in place.
WARNING: DO NOT run the A/C for long with the motor at a lower speed..
Set the fan to 'on' and have someone monitor the furnace blower. Go outside and hold the AC contacter down for as long as you're willing to. If the furnace blower never trips out, then it is that contacter getting hot and drawing an over current. Otherwise, happy hunting; that's my two cents.
You could also try toggling the fan to 'on' a bunch of times and see if that does it (could be a hard start after all; old motor/bearings). I guess if you want to freeze your unit and check that contacter at the same time (without anyone having to stand there) pull the power feed to the blower motor (from its clips on the control board) and call for AC. If it never trips out, it was the blower motor. If it does blow out, then it's somewhere between the control board, that contacter, or the thermostat and its wires (have fun ;).
Best Answer
Shorting one of the thermostat wires to ground might have tripped the breaker on the 24 VAC transformer that powers the thermostat.
Another option is that you damaged multiple wires but only the white one badly enough to notice it.