Runs good until i turn air condition - 2004 Chevrolet TrailBlazer

if you live in an area where its always hot

I am not familiar with your model, but the "rule of thumb" is :
The radiator fan "to cool the engine" will run until the engine temperature has cooled sufficiently to allow the temperature sensor to kick off.
(That temperature sensor is screwed into the engine block.)
This may be as little as a minute to as many as 5-8 minutes.
If your car had air conditioning, that would be yet another fan, that should run only when the air conditioning is turned on.

Does the fan really run until the battery goes dead?? OR are you afraid that it might run until the battery is dead?? In many cars, the fan will continue to run for a short time after you shut it off.... until the engine coolant is cooled to a certain point. It can also run for a while when you've been using your air conditioner. Now, if it is actually running continuously and won't turn off, there is a sending unit somewhere that isn't functioning correctly, either in your cooling system... or your air conditioning system. You're going to need to do some research and find out which sending unit might be the culprit..... or take it to the shop. They'll know what to do and can probably quickly fix it.

Check the condition and operation of the following:
1) Spark plugs, leads and coil(s)2) Air filter3) Fuel filter

Check condition of spark plugs, fuel filter and air filter.
Check condition and/or replace plug leads.
Strip clean and inspect idle control valve.

Report if no fault found.

whats the fuse for. if it operate the air conditioning system on the engine fuse box ur compressor clutch is burnt. if its the fuse inside the car it o\powers the hvac controls. put a new fuse on unplug ur compressor clutch connector and turn the engine on switch your air conditioning and heating controls on and off see if it blows the fuse again if it does then u have a problem with ur inside wiring circuit or heating ventilation air conditioning controls. good luck.

BACK IN 1984 NISSAN HAD THE ELECTRONIC IGNITION WITH AIR GAP ADJUSTMENT.YOU ADJUST AIR GAP IN THE DISTRIBUTOR BY LOOSENING THE STATOR MOUNTING SCREWS .MOVE THE STATOR UNTIL PROPER GAP IS ACHIEVED.THIS COULD BE NO SPARK CONDITIONS.

Cant be good abd could do damage.. I would take no chances.. If the noise came right after deal work,, take it back and have e'm check it..

When the engine is not running the belt is not turning the ac compressor which will not blow cold air unless ac pump is running so engine has to be running

Does the car have the check engine light on? Verify the air control valve for proper operation, it only works when the ac is on.