Adam and
to AP
I don't have the schematics in front of me, but I would be checking the fuses first. you need to make sure that other coils are not firing.
Power Supply Board - F5 and F6 are the solenoid fuses. I suspect there would have to be more than just the coil on the Drop Target.
PPB board (lower left hand board) - F6 5S SloBlo
If it is not the fuses, then you have two faults that might be simple.
does the trop target register as a score ? Do the Drop Targets pop up at the start of each ball ? If so, there's a switch that is not working behind one of the drop targets. There's also a connector for the entire assembly. you can check that it has not come loose.
The Death Star is operated by a motor. From memory, the motor is powered by a relay which develops dry joints over time. I'd be following the the motor wiring to see which relay is responsible.
You can run the game in diagnostic mode - do you have the manual that would describe this process ?