When I had an entire column down in my System 6 game there was a switch with a broken leg that was grounding the column and making it look like all the switches on that column were always on. Do a visual check on the whole line and check for any shorts as that could be a potential super quick fix.

Disconnect the switch connectors from the driver board to isolate the wires/switches from the transistors/ICs. Now you can use your meter to test the wiring harness to verify there is no short from ground to any row or column on the wiring harness. If that checks out okay then it's something on the driver board. Nice detail on how to diagnose this can be found here:
http://pinwiki.com/wiki/index.php?title=Williams_System_9_-_11#Switch_Matrix_Row_and_Column_Testing

As for testing transistors there's a nice guide here:
http://www.pinwiki.com/wiki/index.php?title=general#Testing_a_Transistor.2C_Silicon_Controlled_Rectifier_.28SCR.29_or_Field_Effect_Transistor_.28FET.29

From that guide on a sys9 board switch area you should have 2N3904s:
NPN TO-92 package (2N3904, 2N4401, 2N5550, 2N5551, 2N6427, MPS-A13, MPS-A42, PN2222A)

Place the red lead of your DMM on the center leg of the transistor
Probe each of the flanking legs with the black lead
.4 to .6 volts is a normal reading
Readings outside of this range indicate a failed transistor