I bought an 86 T/A about a week ago. Solid ride, underbody looks brand new, next to NO rust. Interior is a little rough, but the real problem is under the hood.

Car was REALLY cheap, so I bought it despite its issues. At first, it wouldn't idle at all, but it started easy. Started poking around, found the vacuum advance line was gone, and one plug wire was broken. So, we tore in and:
Fixed the broken vacuum line
All new plugs (properly gapped)
All new plug wires
New fuel filter
New air filter
New battery

Now, the car will only start if you hold it at WOT. It idles, a little rough, at about 800 rpm, flutters up to 1k and almost to stalling (400 rpm). If you put it in gear, it comes close to stalling, and "surges" against the brakes.
While driving, it has low power, and seems to dump when it shifts, almost stalling.

The engine is a 305 TPI, though it is supposedly a 350, I doubt it. If it was a carb, I'd say it was flooding out, but how to fix a TPI that is doing it? Is that whats going on? Ideas, thoughts?

 

Sounds like a lean fuel condition to me. Check for a vacuum leak. Get an ohm meter and test the resistance on each of the fuel injectors they should all be ~14 ohms. Get a fuel pressure gauge and check the pressure at the fuel rail, should be ~40 psi with the key ON, ~44 psi with the engine running and vacuum line unplugged from the FPR.

 

Allright, verified the injectors, checked the FP, and fixed about 5 vacuum leaks. Now, the car won't idle at all! I still have one unidentified vacuum leak to fix.

 

Have you checked the timing?

Also, it's good to replace anyway, but the fuel pump relay and MAF relay at the driverside firewall. They are like $12 each at AutoZone. Part Number is 912210.

Also, my charcoal canister hoses were reversed. So instead of collecting carbon, it was throwing it right back into the motor. So that's something to check and make sure.

And you didn't mention it, but a new distributor cap and rotor would eliminate those as a suspect and make it run smoother.

Also, check the Throttle Position Sensor ( TPS ). It's sometimes a problematic peice. I don't know where it's supposed to be at.