Have a look at page 2-50 and 2-51, and 2-53 of the manual here http://www.ipdb.org/files/4338/Williams_1997_No_Good_Gofers_Manual.pdf
In solenoid test mode, see if your trough will serve a ball for you. If it won't then check for broken wires on the coil lugs. Also check resistance across the coil, shouldn't be 0 (shorted coil), shouldn't be infinity (broken coil). Should be just a few ohms. If the coil seems good, then suspect the connector at J133 or J113, or the transistor Q44.
In switch test mode, see if the Jet Popper and trough switches are registering. If not, then you have a column of your switch matrix out. Could be the connector, could be the U20 chip. If the column is out, then I'd start by replacing the connector because that's easier, and if that doesn't help, then replace U20. If the column is not out, then test Q44. If Q44 is bad then replace it. If it is good, then replace connectors J133 and J113.