A1J1 on the MPU (from power supply) can cause intermittent booting problems like you describe.. i have the same issue with my Buck Rogers where it sometimes wont boot up until i reseat the A1J1 connector, (one of these days i'll actually get around to repinning it)   try repinning that connector.

Personally i would be doing ALL of the connectors and be done with it.. it really is the only way to ensure reliable operation and will most likely eliminate the problems you're having. Also make sure the connector contacts on the boards are clean if they havent already been cleaned.