Sys3 flippers are relatively simple as they never went to a full digital flipper system, rather using a sensor board to determine when the flipper buttons are pressed.

It looks like your flipper is wired correctly, though I can't tell how the cap is wired (should be across the switch.) Assuming this is a new coil and diode from PBR. Best to check the coil resistance. Might be a bad diode or cap. Also check wiring to make sure there's no short elsewhere in the chain.

viperrwk

You'd have to remove the diode to check it and at that rate you might as well put a new one on.

You should also check the points on the Q relay in the bottom of the cabinet. This energizes the flippers (and the other interactive playfield coils like slings and pop bumpers.) While this is probably not the issue it's always good to check this relay on any new machine/shop job.

Coil resistance, diode, cap, including where it is hooked up and wiring. Has to be one of these.

viperrwk

The Q relay provides power to the two pop bumpers, two slings and three kicking targets as well as to the flippers. One set of points feeds the right flippers, the other set of points feeds the left flipper and all the aforementioned (though the points are bridged on the relay side).

If both sling coils melted, you may have a short somewhere else that could be causing your flipper and sling problems.

viperrwk

Stargate playfield coil schematic