Trough: Most likely problems are the leftmost (drainmost) switch and the exit switches. There are two, since DE decided to have the neat gravity-fed trough require an extra kicker to get the ball to the shooter lane. On my game, this switch was slightly out of adjustment, and the game couldn't see a ball in the staging area. This caused a lot of weirdness.

But that's secondary to the flippers being dead. Get a multimeter. Make sure there is +50V at the flippers. The flipper coils have a diode. If you ground the non-banded side, you should see the flipper kick. (Don't do this for long, it heats up the coil.) Make sure all the fuses are good; since all the flippers are dead, something in the power supply is most likely not working. The flippers are driven from a PCB in the cabinet. IIRC it must be plugged in for the switches to register, but make sure its high-power fuses are all good, and it's getting +50V. You should also be able to ground the tabs on the transistors here to see them kick.

But since none of them are working, and both switches are working, check for voltage.