sometimes a wire breaks on the shifter from moving the shifter into the gears that controls the solenoids. in my case it was the yellow wire on the shifter.

 

Ok right on. Does the shift column come off fairly simply?

 

the break usually happens on the console shifter wires not the column itself.
here is a pic of the plug that goes into the console shifter lever with the pulled yellow wire
you have to remove the shifter handle and pop the shifter cover to get to the shifter.

 

Hummer has a safety feature to make it idiot-proof. When parked, shift the floor shifter farthermost forward, rotate ignition key to the off position and remove. Done! Failure to perform above, could cause your Hummer to roll away.

 

This is the wiring diagram for the ignition interlock actuator circuit for the '07.

The Owner's Manual for my '09 says "This vehicle is equipped with an electronic shift lock release system. The shift lock release is designed to: Prevent ignition key removal unless the shift lever is in P (Park) with the shift lever button fully released"

Occasionally, the key on my '09 will get stuck in the ignition, but I've found that pushing and releasing the shift lever button a few times will energize the solenoid and release the key. There's probably a 2 cent spring in there that gets weak with age. My guess is this switch is the most likely cause of your problem. I haven't been able to learn where the switch is located, but I bet its in or close to the button on the shift lever.

If its not the switch you will need to dig a little deeper. The circuit is pretty straight forward, but relies on the retained accessory power to work. That's the feature that lets you listen to the radio and run the wipers after you turn off the car. If your radio works when you turn off the ignition then shuts off when you open the door then RAP is working and you should move to the next step. If RAP is not working try swapping the RAP relay with one of the other relays in the fuse box. If RAP starts working, the relay is your problem. If RAP still doesn't work then the BCM is probably not providing the switched ground signal to the RAP relay to energize and activate RAP.

If RAP checks out, check the grounds connections on the right inner front wheel well inside the engine compartment and make sure they aren't all corroded and there aren't any broken wires. IIRC, the grounding terminal lug is just in front of washer fluid reservoir.

If none of that pans out, then I would do as bronxteck recommends and check out the wiring for the shifter under the shifter console.

Happy hunting.