Since your batter died, it also cleared the PCM memory. The computer has to re-learn. One of the little tricks I remember after re-setting the computer is to do the following:
Clear PCM Memory (Pull battery or it's easier to pull three connectors off of PCM.
After restoring power, turn the key to the "ON" position but don't start it. While the car is on, slowly depress the accelerator to full throttle and then release. This allows the PCM to learn the throttle position a bit. Do this three times. Turn the ignition off. Then go ahead and start the car. Let it idle for a few minutes before heading out.
Cleaning the IAC motor is not a bad idea either. But the biggest issue is that the computer needs to re-learn to operate the IAC motor so that the engine doesn't get starved of air after you let off the gas pedal.
One thing I noticed when messing with the throttle position switch is that it requires some tension to be installed. This tension on the switch correlates to about 17% throttle position. Full throttle is about 84%. It wasn't 0% for idle and 100% for full throttle as I expected. I always wondered if this was one of the reasons the computer needed time to re-learn how to properly operate the IAC valve.