Please try this: You need to clean the throttle body! I have an 2002 did the same thing every time I disconnected the battery, had to actually keep my foot on the fuel or it would die... Now it will relearn the idle but it takes several days ( I noticed each time it has taken longer to relearn).. I just tonight cleaned the the throttle body.. disconnected the battery etc.. My husband just finished up and took it for a drive and it for the first time in a long time idled without having to keep my foot on the fuel and he stated "Its ran the best it has in a very long time" If I where you I would get on youtube and do some looking around!! Also its very easy to take off and clean!! Good luck!
Here I took this straight from a youtube video.. This guy listed pretty much step by step.. Hope it helps:
Trailblazer (Envoy, Bravada) idling issue, even worse when turning on the AC, the car would just completely shut off. Would go below 500 RPM.
Simple solution, clean the throttle body, connected to the electronic idling motor.
This is a 2004 Trailblazer with the 4.2 inline 6 cylinder engine in it, but this issue is common with the whole generation, 2002-2009 (1st generation Trailblazer, and other vehicles with the same engine/throttle body/electronic idling motor).
Simply...
First disconnect the positive battery terminal connector screw and separate it from the battery. (important step)
Remove the metal strap holding the intake hose to the throttle body and remove 2 screws holding down the plastic intake box.
You will then see the throttle body connected to the electronic idle motor (one piece).
Next remove the harness connected to the top of the throttle body/idle motor. Then remove the 4 screws holding the throttle body/idle motor in place. The throttle body/idle motor then will be completely removed. Clean the inside of the throttle body with carb/throttle body cleaner, a few bucks at your local auto store or even walmart. Clean it thoroughly, blow through the small hole on upper side as well, has a tube coming out one side. Spray it a bunch till you see no grease/oil/gunk in it and wipe it down good.
Next replace all the parts that were removed. Remember to reconnect the harness connector going to the throttle body/idle motor.
DO NOT start the car yet.
Next you have to reset the PCM (powertrain control module), you do this be still keeping the positive battery terminal disconnected and open the fuse box and remove 2 specific fuses that go to the PCM. For the I6 (inline 6 cylinder engine) remove fuse 10 and 28 as shown in the video. With the battery and 2 fuses disconnected wait a few minutes then reconnect the battery as well as the 2 fuses.
Make sure ass the connector and hoses that you disconnected are put back together then start the vehicle up.
In some cases the vehicle may still act weird a little but sometimes it may take a few drives, even days, to have the electronic idle motor to reset itself. Once it does the car will be running smoothly, even with the A/C on.
