After reading up on the system 1's, they seem like a real PITA compared to a Bally/Sterns.
Question: Did the seller seem like he knew anything about pinball machines? Often, they will say the flippers don't work, but they may not have even removed the glass to check the rest of the solenoids. They just don't know any better. On these early Gottleib games, it might be something as simple as the coin door slam or roll tilt switches being "open", which will cause the game to not boot up. Try and close the switch and see if the game boots up. Especially if they are really corroded.
Funny stories kinda on similar topic.
My roommate's girlfriend called him up crying because her car wouldn't start and she didn't know what to do. So we drove the 45 minutes to the mall and after about 15 minutes of tinkering around, found out she left the car in Drive when she shut off the engine. We put the car in Park and it started right up.
My Grandmother couldn't get her steering wheel in her car to move so she called me and I drove to her house. Car started right up. Steering wheel turned no problem. My guess is she didn't push in the brake pedal so the steering wheel was locked. We took her keys away later that week to save lives.
Moral of the stories, "some people aren't very bright." But most people just don't have the knowhow or inclination to troubleshoot. Hopefully you get a hidden jem because the old owner panicked when "it wouldn't work right."