i found this i dunno if it helps becuase yours is an 03 GM Service Bulletin No.: 05-01-39-001A
Subject:
Blower Motor Inoperative or Intermittent, Blower Speed May Drop or Blower Continues to Run After Key Off (Install a Capacitor at Blower Motor Control Module Connector)
Models:2004-2005 Pontiac Grand Prix
Condition
Some customers may comment on an inoperative or intermittent Heating, Ventilation and Air Conditioning (HVAC) blower motor. Others may comment that the blower motor speed may momentarily drop or that the blower motor continues to run after the key is turned off.
Cause
This condition may be caused by a voltage spike from the wiper motor. The voltage spike may cause a logic lock up in the blower motor control module that may be either momentary or permanent.
Correction
Install a capacitor at the blower control module connector.
DO NOT replace the blower control module, blower motor or the HVAC Control Head
