The root cause of that is not the AR itself, but rather the edge connector fingers on the game boards getting a layer of oxidation built up on them. This issue has been discussed in many threads here, and is common to Atari games.
If you get the AR's rebuilt without fixing the root cause, it'll just happen again eventually.
The solution (in addition to replacing that burned 10-ohm 1/4 watt resistor, and replacing the 2N3055 bottlecap, which should be done on all original AR's) is to get a fiberglass pen and some DeOxit, remove and separate both boards in the game board stack, clean all fingers with the fiberglass pen until they are shiny, clean the residue off with Goof Off or isopropyl alcohol, then apply DeOxit to them. Links to what you need below.
PS - I also refurb AR's.
SCRATCH BRUSH FIBERFLASS BRISTLE. ð¢ The pen style brush works simply by gently twisting the cap to extend bristles to the desired length and bristle stiffness. to retract when not in use twist the cap in the opposite direction.
www.ebay.com