2010 HHR LT 2.2 has CEL codes : P0717, P0700, P0976 & P2764

New starter, battery, spark plugs (41-103) new filter & intake hose. Cleaned mass air flow sensor. Transmission shifts perfectly. Surging while driving and occasionally stalls. Occasionally won't crank. Occasionally when turning the car off I can completely remove the key with switch off and engine will still run for a few minutes. All gauges going crazy constantly and dash lights flicker.

 

I suggest you have the battery load tested, and the charging system tested also .

 

Has the ignition switch recall been done?

All of those codes are for low voltage to a sensor or solenoid. That usually means a loose wire.
What was happening just before the codes popped up.
I would try unplugging the TCM and inspecting the pins then put some dielectric grease on it. And inspect all of the wires that end up in the transmission.

 

According to my vin all recall replacements have been made already. I didn't have the car then. It's been fine for the 2 years I've had it. The night before the codes came on i got home put the car in park and turned the switch off and completely removed the key and the car still ran for a few mins. After it finally shut off i got out and went in and the next day it's got codes for days

 

I can't think of a connection between those codes and the engine running on. I never heard of an engine running on for minutes after removing the key; maybe a sticky run relay (#51 under hood). Make sure fuse #25 on the BCM and fuse #43 underhood are seated.

These are the only points of commonality I can find: TCM connector, run/start relay and the 2 fuses cited above.

 

Hmm. I wonder if you mistook the cooling fan running for the engine still running ?
If the car was running hot, the cooling fan will run after the car is shut off.

 

You HHR is a 2010, so I’ll suggest this again.
load test the battery and charge system .

 

Its definitely not the fan running... when it does it i can pull it out of park and drive the car... without the key. It has a brand new battery just bought it 2 days ago.

 

You should not be able to do that, for that issue the ignition lockout is out of wack or broken.
Drive it to your local GM dealership have them confirm the ignition lock cylinder and switch has been addressed by the recall.
It may also relate to the shifter if an automatic transmission, not locking out the ignition