One problem related to transmission solenoid has been reported for the 2010 Chevrolet HHR. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2010 Chevrolet HHR based on all problems reported for the 2010 HHR.
In a parking garage on the 4th floor. Backing out of space. While backing up, I hear a loud boom. Nothing behind me. Thought perhaps a tire failure. Put vehicle in drive to pull forward out of traffic lane, and the engine accelerated uncontrollably. Brakes wouldn't respond. By the grace of g-d or reflexes, I turned the wheel to the right to avoid flying through the guardrail and off the 4th story of the parking garage. Vehicle came to a halt when it smashed into a concrete support pillar. Both air bags detonated, passenger-side air bag apparently broke the windshield on that side. Engine shut off. Lights in passenger compartment turned on, hazards started flashing on/off (couldn't turn them off). Waited for tow truck for 5 hours. Tow drivers had to jump battery - couldn't get front hood open, back door electronic lock non-functional due to dead battery. Tow driver climbed inside car, removed inside decking to access battery. Tow driver jumped battery, attempted start. First two or three times, it wouldn't start, eventually on the 4th or 5th time it started but the engine was racing again. Tow driver put car in reverse and it flew backward (I thought it was going to go off the deck of the garage backwards. . . ). He stopped the vehicle, turned the wheel and headed forward - it shot down the ramp until they got it out of the garage and on the truck (I was outside the vehicle watching from a safe distance while he did this). Vehicle totaled. Not sure what the problem is/was, but I'm lucky to be alive. Have heard of issues involving stuck idle solenoids, drive train problems, etc.