Have you tried repinning the cables? The IDC connectors wear from constant plugging and unplugging and either the wire connections to the very small crimps break or the gas tight seal is lost and develops oxidation. As the current heats the small resistance, the resistance increases (thermal runaway). This is why it can work during a cold power up, but fail as the game runs. The fact that the displays come on briefly while wiggling the connector is a fairly good indication these need attention. You could also have cold or cracked solder joints on the header pins, so if repinning the cables doesn't fix it, remove the MPU and inspect/reflow the reverse side of the board connectors.
http://www.pinrepair.com/connect/