Hi Scott,
Welcome aboard ! it sounds like the wire you replaced from the battery, was probably the "fusible link". If it was thicker, you would probably have described it as a cable.
Not sure whether a 34 year old Starlet had any form of reverse polarity protection, built in, on things like the EFI controls. Generally, electronics does not take kindly to have reverse polarity applied. You need to go through everything electrical in the car, with a check list, of what still works, & what does not. That may provide some additional clues. Horn, lights, gauges, fans, etc. My guess is that it will electronics failure, most likely. As the main electronic device is the ECU, & it is the engine that will not run, then that is probably the culprit. Remember, the EFI Starlets had conventional distributor ignition, so that will be why you obtain a spark. The ECU, to my knowledge, has no control at all over the ignition system.
The only quick & simple way to know whether the ECU, is your issue, is to substitute with a known working one.
P.S. If wires going to the injectors are hot, then either the injector coil has failed or the driver that fires the injectors have failed & are permanently on.
Cheers Banjo