Differential
Had the same symptoms on a '99 Burban. Turned out to be a bad inner axle bearing. The drive shaft will transfer the grinding sound to the trans area. First check to make sure all the U-joints and CV are solid. If yes, then go to next easiest/cheapest check. Crack open the differential cover. Lay a pan under it and get ready for the bad smell. The fluid will sink. Check for metal shavings in fluid. If yes, then inspect closer to see if the bearings holding the axle ends are solid(both sides). Try to lift differential with a pry bar, it should not move. If it does, you have a bad bearing. The differential can rotate, but not move up & down. If these check are all negative, then check the Pinion shaft bearing. Try to lift/shake drive shaft where it enters the rear axle. It should not move. If it does, bad Pinion bearing. If all these checks are negative the move farther forward along the drivetrain looking for anything that is loose.
It took me about 2 hours to change out my differential(locker) and all bearings and seals. Cost: $550.
When you close up the differential cover use a new gasket and coat it with "Copper Plus" high temp gasket seal. Great stuff, has never failed for me. Next, there will be plug on the side of differential that should take a 3/8 drive(square). That is the fill hole. Fill with differential oil until the oil starts to come back out the hole. Replace plug. You are done.
