grinding noise

[2002 F350]

So for a while now my truck has made a weird slipping/grinding noise but it only happens as low RPM when im taking off from a stop. Now it doesnt happen all the time but some days are worse then others. Some times ill hear it really bad for couple days and other times i wont hear it for a week or two. I cant remember when it started but i was wondering if it has anything to do with my truck being rearended. It was parked and a drunk driver smashed in to the rear doing about 50-60 mph i replaced rear end drive shaft truck bed and didnt know if something in the transfer case or transmission has broke or cracked. If im stopped on a hill and taking off slow it will make the noise 3 or 4 times then i wont hear it again i checked oil and its a little dirty not bad but does not smell burnt any help will be great

[back woods]

manual shifted transfer case? shift fork might have been tweaked when the drive train was compressed causing the fork to wander a bit between 2wd and 4wd. Just a guess, one of my trucks has a shift fork that is about out and it sounds absolutely horrible. could be the transfer case moved and the linkage stayed in one position.

[2002 F350]

The 4wd is the electric shift idk if its any difference... when I switch it over to 4x some times it clunks pretty bad.... when the truck makes the noise it sounds like plates slipping but the rpms never drop..... how would I check the shift fork