Driving on the interstate at 75+ MPH, suddenly feels like a front wheel has thrown a balance weight. Slow down a bit and the vibration goes away but the engine RPM rises abruptly, then goes back to normal. I ease over to the right just as the engine is no longer driving the wheels. Once off to the side, won't move in any forward or reverse gear. Sounds like the tranny might be TU, just replaced with Jasper unit about 20K miles ago at 180K (under warranty). Hit the OnStar button and get the free GM tow to a repair shop.

The shop calls Jasper whose rep listens to the sound over the phone and says it sounds more like the transfer case. We shift to Hi Lock and can drive either forward or reverse - now sounding like the transfer case for sure. Shop gets transfer case on order to the tune of $2,500 installed - BTW GM part is $500 less than Jasper unit..

While waiting for part the shop looks further. They find the front drive shaft boot is missing and the joint is likely to fail soon, so since they're already in there makes sense to replace. Further examination finds the left front axle has backed out and the splines are ground down from the intermittent engagement. So now while awaiting the transfer case, the shop replaces the drive shaft and axle. Gadzooks, the H3 now runs normally in all transfer case modes. Not only that the gas mileage seems to be about 1 to 1.5 MPG better than it was before.

Sounds like that front axle was an issue waiting to fail for some time. Anything else I should be looking at now?

 

At some point an aftermarket front cv axle was installed that was slightly too short and pulled out of the front diff carrier. I am relatively confident you did not need a new transfercase at all. That shop did not understand how all wheel drive works or that the exact symptoms you describe of not moving forwards or reverse is what happens when the transfercase is in all wheel drive mode and you have a front cv break or pull out of the front diff and ruin the splines. If this happens and you need to move the vehicle off the roadway turn the vehicle off, wait for the drivetrain to stop spinning then move the key to the "ON" position but do not start the engine. Then press "4hi lock" to lock the center differential and you can now pull forwards or reverse to get off the roadway to safety and either temp plug the cv back in or get towed and replace with the correct length cv. Same thing happened to my friend's H3 and when I broke the CV in my old 2006 H3

 

Sounds like the front diff went. The Tcase was probably fine.
I would have replaced the front prop shaft like you did with a torn boot.

As atvspeed pointed out. When the front diff goes the vehicle will not move in 4hi. In 4hi lock it will transfer 50/50 power to the front and rear.

 

Shop did not end up replacing the transfer case. Front shaft and left front axle replacement seemed to have it running well - so far anyway.