As you have found, all three balls must be in the trough for the game to be ready to play.
Is the machine is "attract mode" - with the displays cycling through the last game score played and the high score to date ? If not - the game has not booted properly.
Try the test switch on the front door. The switch on the MPU is a reset switch, not a test switch. See what happens when you press the test switch on the front door. The first press should light all the lights, the second test will go through the solenoids and the third will test the displays (might be the other way around).
If the solenoids are playing up, you have a small board under the playfield with a 555 globe and a relay mounted. This board can cause issues, but first lets get the game booting.
At this point, all the boards most likely will be fine, but the old connectors may be the problem. Refit the connectors to the MPU board.
