There are a number of possibilites for why your system has been rebooting. An old power supply board is usually one of the first things to look at. Just because the 3 LEDs light up does not mean that it is working correctly. If you have not done anything with it since the 90's, there is a good chance that it will need a cap kit.
Also the original wiring harness has been known to cause issues of voltage drop from the power supply to the game boards due to oxidation on the header pins, connections to the wire in the connector coming loose and other problems.
The most common problems with switching power supplies and Williams games revolves around a quirk in the 6800 family of CPUs and the CMOS used to store high scores and game settings. When the supply voltage to a 6800 CPU (the Williams boards use a 6809 which is in the same family) drops below a threshold value (typically 4 volts or so), it begins to write random values through the memory space. If that write happens to hit a ROM, it is ignored, they are ReadOnlyMemory anyway. If it hits RAM, no problem, the RAM will be refreshed the next time it is powered on anyway. If it hit the CMOS, ooooohhh Mission Control, we have a problem! That random write could change the number of lives you get when you start, change it out of free play, wipe out your high score table, etc. The answer the Williams engineers came up with was to stick a large capacitor on the +5V power supply and to add a CMOS write protect circuit on the MPU boards that triggers when the 12V unregulated power drops. When the power is shut down, the big capacitor drives the CPU for a few miliseconds after the 12V unregulated goes down. This gives the CMOS memory protect circuit time to kick in and protects your game settings and high scores. Switchers do not have that time delay. When +5V goes down, the +12V goes down at the same time, which does not always give the memory protect circuit time to kick in. If the CPU spews into the CMOS area, bye bye saved stuff.
The other reason there is some hostility towards the vendor you bought from is just that he plays on the ignorance of non-technical users. He is right that new RAM and a new power supply will fix a significant number of the issues some of these older games are having. Much the same way lifting up the radiator cap and sliding a new car under it will fix most car issues. It is overkill. The original power supply lasted 25+ years. With a little rebuilding, and $10 or so in parts, it should last another 25 years. We won't get into the ethics of selling you $12 worth of RAM, $5 worth of wire and $15 worth of power supply for $90 plus shipping for something that will sooner or later trash your scores and/or settings

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ken
PS: Dockert and I both rebuild Williams power supplies if you don't feel up to the task. PM us fr details. Otherwise, Bob Roberts sells rebuild kits that cover the basics if you want to try it yourself.
You don't have your location in your header, so it is hard to see if there is anybody else near you that can help. Poke around in your profile and you can see where to set your location, believe it or not, that does help.