You can test the connection between driver board and solenoids very easily by attaching a wire to ground braid and then touching the metal tab of the transistor with the other end of your wire, this will run the transistor to ground.. do this on the kick out coil and see if it fires.. if it does then all well and good.. the path from transistor to coil seems fine. If it doesn't then the fault more than likely is elsewhere and could lie between the signal to fire ( from CPU) and the driver. Take note though that when you do the tab test it determines the very last stage between driver and coil and so your fault may be before this which is either a faulty IC or signal connector fault. what the guys here are saying is 100% correct and to completely eliminate the fault you really do have to do the laborious task of repining the connectors and then maybe some more... it could be the connectors and often this is the case... your signal to and from CPU are the irritating ones on the RHS which you haven't done yet.
you could also have a fault with a buffer chip.. or a PIA etc. But before we get complicated.. do the mechanics and then if no luck we venture further