There are often switches on one of the power rails that separate the always working parts (e.g. coining up, reset, etc.) from the rest of the game that is only powered during a game (scoring, etc.). The Hollywood schematic on IPDB for example shows switches on the Game Over, Tilt and Start relays that all need to be closed for the game to play. It seems likely that one of those switches is open.

But if that were the case you wouldn't have voltage across the flipper switches. How are you measuring that?

/Mark

Here's part of the Hollywood schematic which is probably similar to yours.
Williams flipper swtich voltage (resized).jpg
If you measure from the 30/yellow wire lug on the transformer to the 80/black wire on the transformer you'll measure about 50 volts AC. If you move the meter probe from the black wire on the transformer to the black wire on the flipper coil lug (or any other coil lug) you'll still get 50 volts. If you move it again to the 86/black-brown wire on the flipper button switch in this schematic you'll still measure 50 volts between that and the 30/yellow wire. All that really tells you is that the wires and flipper coil are good. It doesn't tell you anything about the flipper button switch.

If the Game Over relay switch in the schematic is open and you measure the voltage across the flipper button switch you won't see 50 volts because even though there is a path back to the transformer through the flipper coil, there is no path in the other direction to the 30/yellow wire on the transformer that would complete the circuit.

I suspect if you were to jumper around the Game Over relay switch (and any other switches between the 30/yellow wire and the flipper button switch) that the flipper would start working.

I'm sure Mark has you on the right path. Just thought I'd mention that my experience with Williams games with the blade style jones connectors have been finicky at times. Even when fully seated and properly cleaned.