You can do all of the trans tests, may find problems, but not likely to solve the main problem. Looking at the posted clues, this is one of the most important ones.
The auto trans is effectively in neutral when the motor is off, this is why they have a park pawl. So the park pawl has to be on the output of the trans. For the park pawl to skip when engaged, that drum is spinning. To be spinning, the trans has to be working and something is disconnected between the trans output and the wheels. In this case, the driveshaft isn't spinning, so has to be between The trans output and the drive shaft flange, in other words, transfer case or trans output shaft broken or splines stripped.
The next clue is; shavings and low/no lube in the transfer. My experience says the transfer should be clean, have never seen one with debris that wasn't toast. My earlier reading of the post interpreted that the plugs were pulled and nothing came out, but shavings were found? Now looking, the fill plug may have been all that was removed? If so, my next step would be to remove the transfer drain plug, see what comes out, is on the magnet. If the fluid/magnet is clean, look elsewhere, if there are chunks, likely found the problem.