'07 HHR the engine temp gauge only works some of the time - when not working the heater still works but not the A/C. If the engine temp gauge is working the A/C works. The engine light stays on for no apparent reason and the left rear passenger door lock no longer works with the rest of the door locks

 

pull the code from the check engine light to start with. have you checked a fuse for the power locks?

 

It was a damaged thermostat that was causing the engine light to stay on and the engine temp gauge to not work.
The thermostat was all shot to hell, stretched out, torn and missing some pieces. After I replaced it the, temp gauge started working again and the engine light went out after I had driven about 24 miles and has not come on since.