The most common problem I've seen with these has been the ignition switch. That having been said, I've also seen more oddball causes for ignition voltage concerns on the trailblazers than most other GM vehicles. Have a look at the following, and in addition, you might take a look under the fuse block under the rear seat and see if you have any chafed wiring.
The following diagnosis might be helpful if the vehicle exhibits the symptom(s) described in this PI.
Vehicle may exhibit a combination or all of the following symptoms: ABS light on, Red BRAKE light on, Service 4WD light on, HVAC blower motor inoperative. Various DTCs may also be present.
Diagnose for loss of battery voltage to the rear fuse block on circuit 300 ORN for the following fuses:
Note: Prior to proceeding forward with the information below, it is important to verify the voltage as indicated however it is equally important to verify the integrity of each circuit. This can be achieved by performing a voltage drop test or by adding a device to each circuit that will supply sufficient load to verify the circuits integrity.
HVAC 30A, 4WD 15A, HVAC 1 10A, BRAKE 10A, TBC RUN 3A.
1. Check circuit 300 ORN for battery voltage when the ignition key is in the RUN position.
2. Check for battery voltage at the rear fuse block under the rear seat Connector C1 pin D9.
3. If battery voltage IS NOT present at these locations, check for voltage at the ignition switch pin G for circuit 300 ORN.
4. If battery voltage IS present at the ignition switch pin G, check circuit 300 for an open.
5. If battery voltage IS NOT present at the ignition switch pin G, replace the ignition switch.