That’s normal. Nearly all Gottlieb EMs from the ’70s have only lights lit in the head and the tilt light illuminated when you flip the power switch.

The labels on the transformer can get slow-cooked over the decades. Looking crispy is normal.

Have you tried to start the game by pressing the replay button on the coin door? Does it have any credits in the replay window?

What happens when you manually actuate the S Relay?

Here is the startup sequence from Jumping Jack’s manual.

Jumping Jack Startup Sequence

Because your S Relay is not making the score motor run, here are the things you should check:

Bounce switch (next to the score motor)
15-amp fuse (mounted on the wood panel next to the tilt bob)

The switch stack on your replay unit is perilously overextended. The stepper has stepped too far, pushing the peg against the bakelite separator to the point where the bakelite could snap.

The top coil on the replay unit will step it down and alleviate the pressure on the bakelite separator. Do you know how to actuate steppers by hand?

Actuating that top solenoid should step the unit down, rotating it clockwise, moving that peg away from the switch stack. If it did not move, your replay unit might be seized up.

You could remove that peg to temporarily relieve tension on the switch stack. The purpose of that peg is to limit the number of credits on the replay unit by pushing the inside-facing switch open. That peg will need to be put back into place once you figure out why your replay unit is not stepping down.

Incidentally, this issue on your replay unit is likely unrelated to your other problems!