Rip it off and bench test it. Get jumper cables and a battery, hook it up on the bench. If it fires it is definitely good, if it does not fire it is definitely screwed. That eliminates all other wiring issues, since power is directly there. To do this, you need a screwdriver or something to short from the + terminal to the ignition terminal (you need 12v at two terminals to start it), ground the case to the - terminal, make sure ground is good or it wont start. If it works, then check the start switch ( in the columt I believe, correct me if Im wrong). If that is good, open the solenoid and look at all the contacts, make sure they are squeaky clean and that everything works correctly. I had quite a time with my starter, but in the end all is well. Ended up having to replace solenoid, as it would click and click but would not start, fortunately I had a spare from an 87 camry, identical solenoid. If you do need a solenoid, it might be cheaper/easier to find one from that car as opposed to a supra. FYI. Other than that, dont ground the positive wire to the frame, you let the magic smoke out of your positive wire and it wont work (after the fire goes away).
Dont ask...