Hmm, do you have a rom burner that you can use to verify all the roms. I have fixed several frogger boards and several had eproms with bit rot and had to be replaced. Symptoms were similar to what your getting. Usually they would run fine in attract mode but reset when you pressed start button. Just a guess but easy enough to check if you have a burner. Also, I assume you have verified your voltages?
Is this a two board set or single board?