This data is for a 2005 Silverado so it may not apply to your 2004 Sierra as the information coming from GM for the Re-Circulation Operation. The only reason I'm posting it is that there seem to be certain conditions that allow the Recirc to Work... and some that do not:
Recirculation Operation
The HVAC control module controls the air intake through the recirculation actuator. The recirculation switch closes the recirculation door in order to circulate the air within the vehicle. The outside air switch opens the recirculation door in order to route outside air into the vehicle. Regardless of the blower motor switch position, recirculation is available only in the panel and bi-level mode switch positions. Including the OFF position. The mode switch must be placed in either the panel or bi-level position before the blower motor switch is placed in the OFF position. In order to reduce windshield fogging, outside air is circulated when the mode switch is in the defrost or defog positions. If the recirculation switch is pressed into the ON position when the mode switch is in an unavailable mode position, then the recirculation switch LED will flash 3 times. If the HVAC control module detects a fault with the recirc door the HVAC control module will try to drive the actuator for a predetermined amount of time, to outside air, which is the defaulted position for the recirculation actuator.
