Likey it's the soundboard then.
If you got one error on it, that's a good cause.
Essentially, a lot of data lines (not all of them) extend from the MPU to the Fliptronics, Sound, and Display board. On bootup, the MPU expects communication back from the Sound board. Display and Fliptronics boards, no.
Without the sound board in, the bootup will take a little longer, as the MPU gives up asking the board for a status. However, if something on that chain of boards is sending bad data, or there is noise - causing the MPU to incorrectly read/write data - then that will cause an incomplete bootup (keep in mind: Other things will, too!) and cause resets after bootup. (The /RESET line is on that ribbon cable too..)
Data lines stuck high could then cause the Fliptronics board to think the MPU is telling it to activate the flippers. Or tell the 8-driver board to spin the clock, and so on.