Ok...
First of all, there are no empty sockets, right ?? Looking at your pic, it's hard to tell. The large black object toward the upper RH corner looks like there is a chip in it, but I can't tell for sure. Actually, it must, that's the main CPU and the board would be dead if that was missing.
Carefully clean the board, compressed air or one of those dust blaster cans. That board is a mess and something might be shorting.
Clean the edge connectors by rubbing them with an eraser until they are shiny.
For these next two steps, you'll need manual, pdf scans are available on the net, google for it, some searching should find you one.
Look for a "test" switch in the cab somewhere, flip it and start the machine, see if it reports any failures.
Check all your input voltages with a voltmeter. Primarily the 5 volt dc circuits are what's needed for the game logic, those should be darn close to 5. The AC feeds to the board and the 12vdc (if used) should be close, but don't have to be dead on.
Beyond that, I'm going to suggest you have the board repaired by somebody familiar with game board repair. The first pic you posted indicates you probably have a failed rom chip or bad video ram. Since you mentioned you don't have experience fixing game boards, it's best not to try with this one. Atari boards can be a bugger to troubleshoot.
Good luck!
D