I wonder if the servo on the back of the transfer case is either damaged or inhibited?
Only way to find out is to remove it. Get someone to help - take the servo off, hold it in your hand and have someone sit inside the car (engine off, but ignition on, gearbox in neutral) and have them turn the selector from 2H to 4H while you are under the car watching the inside of the servo. If it turns and doesn't blow the fuse, then it might be the innards of the transfer case need attention (possibly a mechanic job unless you feel confident in DIY).
If it does blow the fuse still, disconnect the servo's plug and do it again, this is a wiring test to see if the servo wire might have been snagged by a branch or something and the conductors within damaged. If the servo is not connected and the fuse doesn't blow, the servo is faulty. A wrecker probably would be your best source. If it STILL blows, look at the wiring harness and see if it's been damaged.