How good is the 40 pin interconnect between the CPU and Driver board?
many weird issues are caused by this, particularly if you find nothing obvious with the other suggestions.

That will be a resistor and a capacitor. I dont actually have a system 6 so not sure what values they are supposed to be,also not sure if my Flash even has them. They have either broken off or been removed possibly because one or both is faulty.
The answer should be to fit new ones but check what values they are supposed to be. Best to compare to the other sling or the manual

According to the manual there are a whole pile of switches that score 1000 including the 1-6 targets and all the rollovers. I would suspect one of these is very sensitive and the knock of the ball kick out may be enough to make it connect.
Also remember, always use a ball to activate the switches, not your finger.

I hope you get it resolved, It would be ideal if you had another system 6 board to put in. Firepower happens to be one of the oddities that is not interchangeable with much else.
If there are still Scanbe sockets then I would replace them, Vids bulletproofing guide is great.
Ensuring all connectors and IC sockets are good is a 'must do' on these boards. I had a poor connection on my Flash and every single coil locked on until the sleeves melted and it was billowing smoke, without blowing any fuses
Leon's, or Marcos test roms are really good if you have a logic probe and a PC power supply then you can pretty much test your board on the bench to check all the PIA outputs at least.
If you have someone looking at it please post with an update as I'm sure it will help someone else.
Good Luck.