What would cause a clunking sound coming from the transfer case on a 2004 Ford F-250

The CV joints might be worn and need a new boot or even replacement of the entire part. Or it could also be your motor mounts. The motor mounts could be worn and your engine isn't well secured to the crossmember, causing the clunking sound. ... A damaged parking pawl can cause this clunking sound that you've described.

I'd look at the transfer case first.

it sounds like the transfer case is in neutral good test start truck place trans in reverse slowly try to place back in park if it makes any noise then the output shaft of transmission is turning then problem is in transfer case move that lever back & forth several times this might get it working again

The park locks are big metal teeth that slide into the lock position in holes. when you take off the park brake, they are spring loaded and should ping back to the unlock position. The holes are probably dirty, perhaps sticky, so they stick in the on position until you rock the car and this frees them up. You need to dismantle them and clean ans grease them.

Rock back and forth , take it out of AWD , Put parking brake on shift into Park .

with the transmission in neutral,and on level ground try rocking the truck back and forth manually while working the shifterfor the 4 wheel..sometimes if too much pressure is mechanically on the drivetrain it will not shift at all..also check fluid lever in transfer case..low fluid will cause the shifter to bind up..good luck..

UP TO 3 INCHES

I have had that problem with my wifes car,i called a mobile repair guy to come out and tighten something in the steering column,cost me about $50

you have to unbolt the transfer case from the trannsmission, or u can take it out in one peice just a bit harder. you might have bad u-joints thats causing the loud noise, like clunks.

The noise is caused by the axle button being worn out, this lets the axle move back and forth and clunk, this is a unique problem with C clip retained axles, it is a noise issue but will not fail and cause any more damage, in order to fix it you must have the axles pulled and the diff carrier checked for excess wear where the axle retainning C clip rides, if the carrier is ok then replace the axles.