Those aluminum IFS front diffs are pretty weak, but I don't believe the
dealer is telling you the truth. Unless they actually took the front
diff out, how do they know it's worn out? I have an older IFS front
end truck and there is no inspection cover, the diff splits in half
(right and left sides) before you can inspect the ring and pinion. If
the ring and pinion were bad, it would make a hell of a raquet for some
time before locking up. You would hear a whine at first, then as the
gears eat each other up the noise would change to grinding and popping.
I've got a 6 inch lift and 35" tires on my truck so I can attest that
the front diff will take some punishment - and 4000 miles is peanuts.
I have heard of the drivetrain completely locking up before one other
time. A friend of mine was with his father at the dealership test
driving a new Denali and while driving down the street, not too far
from the dealership, the entire thing came to a screaching halt. After
lots of messing with things, they couldn't get the truck to move at
all, so they walked back to the dealership.
Take John's advice - get all four tires off the ground and try to find
out where things are binding. With 4wd engaged, disconnect the front
driveshaft and see if the transfercase will turn freely, and that will
tell you if the problem is in the front diff.
One other thing - if the front diff does turn out to be a problem,
consider buying a used one instead of getting that one fixed. I was
planning on selling mine so I looked for prices on ebay, and found they
were going for around $100 to $150. That's way cheap compared to
getting it fixed, because it cost me around $700 just to have the front
gears changed from 3.73 to 4.88 (nothing broken, no troubleshooting,
etc). Keep in mind I'm talking about a little bit older truck, but
unless something changed for 2005, your front diff probably matches
ones from a few other years.