Hello, Scott... the white wire/red tracer might be intended to be under the ground wingnut..your pic shows another w/r wire there, but is it by chance cut? mine has that color wire grounded.
Also, the coil is fed by a modified flipper power board. The dc to the coil should be pulsed, otherwise the coil (11 ohms) would draw enough current to burn up, or blow it's fuse. If your fan runs and blows air that's not likely your problem, I would look at that power control board. It has a fuse feeding the coil, if someone has bypassed the fuse, or put the wrong size in, your coil would possibly fry. If the transistor circuit that pulses the dc to the coil has failed, or the PIA (driver board) is on constantly, your coil could fry.
Mine kept blowing fuses. The problem was a coil winding in the hypercannon that was shorted to ground through the trigger lock bar (manufacturing defect). Luckily I fround it before disaster.
I can send you schematic shots of the board, or you can find them on IPDB.
As to the loose yellow wire, tomorrow I can take a peek at mine, but it appears to have pulled loose from the relay (white block nearest the wire). Don't hook anything back up until we see a schematic or pics from my machine, tho.