I have a similar problem on my Firepower, and although I think the solution might be different I'd like to spin on from some of the suggesions in this thread.

I have a new PinballPCB driver board (http://www.pinballpcb.com/System3-7DriverBoard.html) that keeps blowing the same IC as yours - IC17 which is a 7406. This occurs - usually after a game or two - when the top left pop bumper is activated. The game tilts and the switch matrix is all messed up until I replace the luckily cheap 7406.

I battled with the problem for some time until I thought I had found the solution. By isolating the lamp wires going into the pop bumper the game started working and did so for a year. Now the problem is back. I have taken the pop bumper apart and further isolated the lamp wire so there is really no way that I think that the switch can short to it now, but the IC keeps on blowing. Which leads me to believe that I just got lucky when I thought I had found the problem.

The PinballPCB board is not a perfect fit for all fours screws in the backbox. I have the two top screws mounted, and the board really just hangs there. The IC which keeps blowing is the topmost to the right here: http://www.pinballpcb.com/images/DriverBoard/DriverBoard.jpg
My bracket is different from the one in the picture though, running horisontally rather than vertically. So my question is, does this board need to be grounded through the screws, or can I just elevate it from the bracket by some pcb feet or similar?

If it is not a problem with the board shorting - can it be the switch itself? The pop bumper switch looks ok to me, but don't really know what I am looking at. Can the resistors on the switch blow? Can the switch short to the coil? Any ideas are much appreciated.

Cheers!