2500HD Front End vibration

[01silverado2500]

I have noticed on my 2001 2500HD 4x4 a vibration in the front end while starting to move from a stop with the wheels are turned. This is with the truck in 2WD and it seems to stop once the vehicle is moving. Has anyone else had this? What can be causing it?

[01silverado2500]

Also I get a slight vibration or slip when backing up on a grade. The truck got a new transfer case installed by the dealer last summer because of an oil pump failure inside the old unit. Could driving with the transfer case messed up mess up any other driveline parts? It is a new transfercase, not a rebuilt one. I just hope it is nothing major cause it is out of warrenty.