One problem related to transmission not engage has been reported for the 2005 Chevrolet Trailblazer. The most recently reported issues are listed below.
At approximately 11:00 am just after parking the vehicle in an inclined home driveway and after turning the engine off for 2-3 minutes and with the automatic transmission in the park position, the vehicle on its own started to roll down the concrete driveway and into the residential street. No one was injured or run over, though the potential was great since my wife and I were both unloading the car from the rear side doors and the tailgate, but we were neither in the doorways or behind the vehicle. Apparently the park transmission lock failed or became disengaged - a serious defect. The vehicle came to a stop in the middle of the street. I restarted the car and have driven it over 100 miles without incident since yesterday. I have used the park position without incident since that time, though I have not parked the vehicle on an inclined surface.