It's your viscous coupler. That part is located in the rear housing of your transfer case. Likely there is nothing wrong with the transfer case itself, these couplers are a wear item and do not last forever. Mine went at 203,000 miles. You can replace the coupler and avoid the cost of a new transfer case. It's possible to replace it with the transfer case still in the jeep, that's how I did mine. Or you can pull the whole unit if that's something you're comfortable with.
The replacement procedure isn't difficult but reaching the snap ring can be a bit tricky with the case in the truck.
The 2004 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2004 Jeep Grand-Cherokee has 56.5 in. of front hip room.
The 2012 Jeep Grand-Cherokee has 40.3 in. of front leg room.
The 2004 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2011 Jeep Grand-Cherokee has 58.6 in. of front shoulder room.
Yes, it is on the front passenger side corner of the engine.
The 2009 Jeep Grand-Cherokee has 59.1 in. of front shoulder room.
The 2004 Jeep Grand-Cherokee has 56.5 in. of front hip room.
The 2011 Jeep Grand-Cherokee has 58.6 in. of front shoulder room.
The 2012 Jeep Grand-Cherokee has 40.3 in. of front leg room.
The 2009 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2007 Jeep Grand-Cherokee has 59.1 in. of front shoulder room.
The 2010 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2012 Jeep Grand-Cherokee has 39.9 in. of front head room.
The 2006 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2004 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2007 Jeep Grand-Cherokee has 57.1 in. of front hip room.