Acts like the brakes are being applied when shifting from Neutral to Drive or reverse?

Here is a video of underneath the truck as you can see it moves fine in neutral but when out in gear or reverse it stops the truck, and I have to accelerate for it to move.

My assumption is perhaps a bad Transfer case? Or driveshaft? I should also mention that there is also a small puddle that accumulates under the transfer case, and I can't pinpoint where exactly it's coming from. It's been like that for some time.

Different angle facing the front half of driveshaft. Loud clunk noise every time it's put in reverse but not any other gear. Truck does not have the front Driveshaft attached but that's not a problem being it's RWD and I don't use the 4x4.

Thanks for the videos, pretty good. It seems like the transfer case is bad, but I would remove the differential cover and inspect the gears to make sure that is not the problem. Since you said the fluid was not good, (burnt) I would remove it and get a used one from eBay and install it. Here is a video of the job being done on a similar truck, (the process is the same):

https://www.youtube.com/watch?v=1Bbvg_DRRow

Also, jack the truck up and spin the wheels to make sure the brakes are not locking up. Go over this guide as well:

https://www.2carpros.com/articles/a-comprehensive-guide-to-fixing-automotive-brakes-locking-up

Please upload pictures or videos in your response of any problems.

I took the driveshaft off and examined the u joints, and everything checked out as well as the yoke. I started the truck up and put it in reverse and there was no more loud clunk sound however when trying to spin the output as shaft while it was in reverse it wouldn't budge in any direction. But with it in neutral it would. I'm in the process of taking the TC out now. Planned on opening it up to see if I can see any potential causes why it failed. Do you have any suggestions on what to look for?

You will know it, but I would look at the chain and the gears with bearings, the fluid will be filled with metal. Here is an exploded view so you can see what you are getting into. Check out the images (below).