Thanx guys, you have given me something to work with. I will use your suggestions.
Always knew this was the best site for help and info.
Hopefully I can figure this out. Which are the grounds for lighting?
Let you know.

 

Driver side strut tower (G109) for left and the driver side radiator support G111) for right.

 

That's great. Thanx donbrew, you're the best

 

Fuses 65 & 66 and relay 71 would also be suspect!

 

Still no lo beams And still get warning that the lights are on when light siwtch is left on,but no lights.
Checked fuses and relay per Oldblue, all OK Cleaned ground connections also.
What VOM readings should I get at the fuse block side of the relay?

 

My opinion. You're at the point now to check the VOM readings at the bulb/socket/wiring itself.
A pain to get to but if it was mine, that would be my next step.

 

Doesn't really matter, something between 5V and 12V. You are checking to see A. if there is signal voltage to energize the relay and B. for supply voltage and then C. continuity from the relay out to the fuse and D. continuity from the fuse to the bulb.

 

Here are my voltage readings, taken at the pin slots for relay 71 in this position.

 

From the wiring diagram don provided, it looks like 2 are hot at all times, third goes to the bulb, fourth is connected to the switch. So yeah, I would think with the relay removed you would get voltages like that.

I thought it wasn't the switch because you were getting the warning chimes. But since the bulbs aren't lighting as DRL's OR as low beam headlamps, the commonality seems to be the switch. If there were a problem with the "hot at all times" wire, or the grounds, it would probably be affecting high beams also. And for 2 separate grounds to go bad at the same time is unlikely.

Or you had 2 bulbs lose the lowbeams, and then bought 2 which also had bad lowbeams. Not impossible, but pretty unlikely.

SWITCH. Headlamp Dimmer. Turn Signal Lamp for Chevrolet HHR (2005 - 2011). #20940099

 

I am confused now. 85 should be ground, 86 should be hot when the switch is ON, 30 should be always hot, 87 goes to the bulb via fuse. Well I guess 85 and 86 could be reversed on purpose.

The DRL relay needs to be pulled to do the testing or 87 may show a voltage.

I would try hot wiring the relay and checking the continuity before dealing with wires.

Here is the internal of a relay.