Welcome to the forum! Try a cold start KOER test and see if the PCM tells you anything.
Try swapping the old IAC valve on and see what happens. If the problem is linked to it for sure, you may have a defective valve or wiring issue. Did you disconnect the battery to force the PCM to relearn?
For the torque converter, verify that the torque converter clutch solenoid is getting power. I have attached a couple pictures for reference to how the solenoid works, electrically and hydraulically. This is from a 1994 manual so there may be minor differences; I believe in 1991 there was a different design for one or both of the solenoids, but similar theory, and the electrical is likely the same. You should be able to check the PCM output at the pin specified in the diagram to see if it is commanding the solenoid. Check for damaged wires as well, maybe run a continuity check from the PCM connector side to the connector at the transmission.
If the lockup solenoid is receiving power, but not operating, the solenoid may have failed. Another thing that happens sometimes is the thin retainer plate holding it into the valve body bends over time and it wants to back out. The SK (Transgo) A4LD Jr Shift Correction Kit includes a washer for this, to help keep the solenoid in place. Anyways, if the solenoid itself is bad, you can replace it. New solenoids are not too expensive but will require removal of the valve body. This is possible at home with no special tools (save for a torque wrench) but will require purchase of new separator plate/valve body gaskets at a minimum. If you go that far, it is a good idea to install a shift correction kit. I have had great luck with the SK/Transgo kit. Had an overdrive solenoid fail one time and replaced it successfully while installing the shift correction kit. Was very pleased with the results. I have ordered all my parts from Transmission Parts USA. They do stock the replacement solenoids, shift correction kits, and Sonnax upgrades, for good prices.
