System 6 games like to toast those resistors. It hardly ever matters. You can replace them, but I do believe they're for lamps.

I would suspect the giant 40-pin interconnect connector between the solenoid board and the computer, because that's ALWAYS bad. If you have Scanbe sockets, those too must be removed; they are either bad now, or will be tomorrow. I would also be suspicious of the giant cap in the +5V supply on the power board.

If you're blowing the solenoid fuse, check for a blown transistor or coil. But no need to do any of that until the 40-pin connector is rebuilt. If the game has been sitting for a decade, it's bad.

Get the batteries off the computer. Look for corrosion.

pinwiki.com should be a good start.

Nice game!

I should note that, the goofy Williams system has the computer's bus replicated across that big 40-pin connector that is sandwiched between the computer and the driver boards. If it's been rebuilt, it's fine. If it hasn't, it will cause the game to have no end of weirdness. (Same with Scanbe sockets.)

The repro boards have a better system with a ribbon cable. http://www.pinballpcb.com/System3-7DriverBoard.html

If you like doing board work, great. If not, I would send both boards out for a refurbishment, and they should be fine. Probably cheaper to rebuild unless there is corrosion I can't see in those pictures.