Sounds like the column 5 and 6 drives are out whereas the column 8 drive is locked on. It’s almost certainly a board problem in the lamp matrix area of the board. Bottom right as you look at it the cabinet. Probably the TIP42s (Q52, Q56 and Q58). Check those.

http://www.pinwiki.com/wiki/index.php?title=Williams_System_9_-_11#Lamp_Matrix_Row_and_Column_Testing

In my experience ...

I have never seen the resistors go bad but there's no reason that they cannot go bad. They are easy to measure so if you're in there just measure it if you want.

A "good" reading on a transistor does not necessarily mean it's "good". A "bad" reading on a transistor means it's "bad".

If you're comfortable replacing the TIP42s then go ahead and replace them. They're cheap. If that fixes your problem then you're done. If not then you'll need to go further upstream to the pre-driver transistor (2N6427) or possibly even further.

The bulbs also likely burned out because they were over-driven by the shorted transistor.

I definitely believe that. After one minute of power those resistors are hot to the touch. My statement was too definitive so I'll retract it with apologies.

I've adopted the policy of replacing the 27 Ohm resistors and TIP42s with "the MOSFET modification" on all System 11 and Data East boards that I have.

If you've replaced the TIP42s and the 2N6427s and they all read identical and correct you need to go upstream. This usually involves a logic probe. You could replace ICs upstream without verification to hope it solves the problem but replacing un-socketed ICs without a reason is risking damage to the board if you don't have the appropriate skills. I do not know your skill level so apologies if you're capable of doing this.

U52 and U53 are the next ICs upstream (see the schematic for further information). These are 7408s. Further upstream from that is U54 which is a 6821 PIA.

If you're comfortable that the TIP42s and 2N6427s are good then I'd recommend getting a logic probe (or oscilloscope) and checking the signals coming off the ICs before replacing any more parts.

The other components in the circuit are the resistor arrays. You can take the resistor readings to verify they are in specification.

There are board repairers on this site that can do it for you but if you want to diagnose the problem further ... try the above as well as get a logic probe and see if the ICs show incorrect signals.