good post Brian!
There's some good posts in this thread, but there's also some wild ass "guesss".
Since it runs on starting fluid, that pretty much gives most of the usuall suspects a pass.
One thing that jumps out is the post about sparks coming from the coil terminal area. That should be investigated thoroughly, and if you have any questions about coditions there, post a pic or two. The terminals down isnide the platic towers should be clean and dry with no traces of burning or carbon dust.
Since it passed Andre's noid light test, I thin a very valid test would be to power the pump up artificially and see if she'll run. That can be doe with dsmlink and some logger setups. It can aslo be doen with the fuel pump test wire that hangs out over by the brake booster.
A fused jumper wire can be run over to the batttery postive termoinal to energise the pump.
If she runs then, it may very well be the ecu can't pull the relay on. Many times the ecu's suffer acid damage some before the caps were repllaced, and it's just now showing up. The residual acid will eat at the board for years if it's not correctly removed/neutralissed. A quick test by substituion of known good ecu will tell that tale.
At any rate, good luck with the troubleshooting, and if you get stuck, don;t hesititate to post up any new questions.
*might be a good idea to stock up on a beer that TurboWop likes so he'll come over and take a look! He's got these cars pretty well figured out and can probably have it purring down to the liquour store in short order.