How is this car, corrosion-wise? Might be a long shot, but easy to check and free to fix. There are major grounding points just in front of the battery, near the high amperage fuse box, and then on the driver's side inner fender apron, in front of the shock tower, and next to the fan control module. You might loosen, and then re-tighten those two 10mm nuts. If you see rust, clean, of course.

Next, on advice of someone who works these quite a bit, avoid the temptation to ever unplug the ECU or SKREEM without disconnecting the battery, first. Otherwise, they can lose sync with each other, causing all kinds of starting problems.

Lastly, the idea about the starter may not be far fetched. Using a starter switch or other suitable method, you can verify that the starter works by jumping the solenoid to +12V.

You've got a tough problem, but almost assuredly, it will be a simple solution. Just a matter of finding it, of course.