With these DC motors, there is no testing it's resistance. If it has voltage, and its not moving, it's bad. That being said, I have had a few evap fan motors short and take out the board. Can't recall a cond fan doing the same, but i suppose its possible. If the motor has any discoloration at all (brownish), replace it. Check voltage coming out of the board to run the fans on J2. GE uses Pulse Width Modulation to run its fans, so you need more than just 12VDC at the motor.
Just my opinion, I'd never pull the shaft of one motor and put it in another. Even if the motor is $200, its still cheaper than a $2,000 refrigerator.
Did your display work with the old board? There was a service bulletin out a while ago on the GE 25cu ft top mount. Basically if you have voltage going to the display/control board, but the main board doesn't receive voltage back, it goes into a 'limp mode' meaning that it could run very erratically. This bulletin doesnt apply to the bottom mount, but its worth knowing. The mini manual on this model doesn't list a specific voltage to run the control board. Check for any DC voltage between all three pins of J4, with J4 unplugged. Plug it in, check for the same voltage at the control board.
While you're at the main board, checking all the thermistors is really quick and simple. Their early thermistors had a lot of issues.
Let me know what you find! Good luck!