I am assuming your claw solenoid driver MOSFET is the beefy looking component in the upper left of the photo. The one with the heatsink. I would test it for shorts. To do this:

Put your meter into diode/continuity mode.
On the component side of the board, put the black lead of your meter on the center leg of the driver transistor.
Put the red lead of your meter on the center lead of the transistor. Your meter should read zero.
Put the red lead of your meter on either outside lead of the transistor. Your meter should read in the .3 to .6 volt range.
Put the red lead of your meter on the other outside lead of the transistor. Your meter should again read in the .3 to .6 volt range.
If your meter reads anything outside the .3 to .6 range, replace that transistor.

If it's shorted, you will get a reading of 0 between the center leg and one of the two outer legs. Reverse your meter probes and it will still read 0 if shorted.

How old is the machine and how often is it used? Your claw coil could be damaged as well, depending on how long it was locked on before you turned the power off. Probably not, as the coils are designed to run several seconds at a time while the claw picks up the prize and brings it to the chute. I would still check your claw coil for signs of overheating and do a resistance test on it.

Also, is there a diode connected to your claw coil? If so make sure it has not gone open or broken off. Without a damper diode voltage spikes can damage or short the driver transistor over time.

If the diodes are shorted, your meter will read 0 in both directions. If they are open, it will read OL (open loop). They seem to be fine. A diode will conduct in one direction with the banded side connected to your black lead.

That's great, you're welcome! It could have just been a poor quality component from the beginning. Glad you got it working. If it wasn't for pinball I would have more trouble tracking that one down.