First, check that the wiring to the shooter coil isn't stretched tight, biting the wire insulation into any metal brackets that might be shorting the coil to ground. While you are looking, make sure that the coil's solder terminals aren't touching anything when the playfield is lowered. You probably put the coil back in exactly as you took the coil out, but the previous technician might have installed the coil in a way that allows for inappropriate touching.

A momentary touch of a coil wire to a metal grounded bracket can pop the TIP 36c, and then it's stuck on... burning up the coil.

The 23-800 coil should read about 4 ohms. If it reads less, like 0.2 ohms, your bad transistor has blown up a second coil which will then blow up the next TIP 36c transistor you put in.

I agree with Frunch.

Q27 is the TIP 122 that drives the TIP 36c that drives the shooter coil. It should measure exactly like all the other transistors around it. I replace TIP 122 transistors with TIP 102, which is a higher rated substitute part.

Q19 is the 2n4401 that drives the TIP 122 that drives the TIP 36c. It should measure exactly like all the other transistors around it.

Beyond these transistors you've got chips that could be the problem, but in my experience problems deeper than the drive transistors almost always present themselves by 'turn the machine on and the coil holds in before the game even boots'. And replacing the drive transistors fixes the problem more than 95% of the time.

Maybe it's just me, but in my experience I very rarely find a bad diode on a coil. Nevertheless, the banded side of the diode should be towards the Vio-Yellow (fat) wire. If you suspect the diode, you'll have to unsolder it, or do what I do, clip it off (taking care not to damage the tiny magnet wires), and put a new diode in.

Let us know what you find!