I am happy to report that I was able to repair the system and I now have it working proper.
Here is what I did,
I started with the wiring and replaced a wire nut that had 8 ground wires going into it. I used a connector and put mating connectors on the connecting wires. Then as I continued my search I found a wire broken on one of the limit switches (soldered on) I re-soldered it and after looking over everything and finding nothing else I could see as a issue, I plugged the unit back in and flipped the power switch and it was like magic. The Y axis arrow was blinking and the coin slot light was ON. The screen went to all zeros and the claw moved to the pay chute (Home) After about 20 seconds I figured out I needed to insert a coin to play. I inserted a quarter and moved the claw away and then to the right and when it stopped the claw dropped then raised with no prize but did return to the pay chute (Home) and opened the claw. The coin receiver lit up again because it was ready to take more of my money... I mean ready for me to try again.
So with that I am now looking for info on things like what should I use to clean the coin receiver and the claw carriage.