Can anyone help me to identify this loose wire I noticed hanging from the wiring harness above the starter? Thanks

 

What doesn't work/ is there a CEL?

What color is the stripe? It looks like black w/yellow.

If it is black w/white the car probably doesn't do anything. That is the main ground that should be attached to the transmission with at least one other wire that goes to the radiator support.

 

I'm with Don. Looks like a ground wire with the loop end broken off. Search around in that area. You may find the remnant of the broken loop under a bolt head.

 

Yes look at the ground wire location on the transmission housing down to the right of the oil filter cap.

 

Could be the reason your HHR was very sick!