Reseat all connectors.
If your old power supply board still works try swapping it to see if that's the problem.

Measure and report back what the 5volts and 12volts measures at the top of the power supply.
There are some test points for measuring the voltages.

Well, being a DE game, I repaired many games that did not boot up or randomly reset during gameplay/attract mode. I suggest replacing the C2 (100 uf use either 35v or 50 electrolytic capacitor) on the power supply. Due to age and heat from the large heat sink that is above it, it will fail at some point. Replace it now and you'll have less issues with your game later.

I have a DE Simpsons also that does the same thing about every 30th game or so. I'll hear a small crackle in the speakers, it resets, and then won't again for quite some time.
I have the original power supply with all new caps and rectifier. I may repin the connectors next. Seems to be common issue with DE especially Simpsons

Monitor your 5 volts on your power supply and I will suspect that it will dip below 4.80v,which will be causing your reset issues. The C2 as I mentioned in the post #4, it will very likely be the cause.

Any luck?

He mentioned a new power supply in the game, and a tech going through the boards, I wonder if he checked the Voltage coming from the outlet?