Jack up the rear, both tires off the ground, trans in neutral. (and front tires blocked please... don't want the truck falling off the jackstands, and rolling away... that sucks. ) Turn the rear wheels by hand. If should feel perfectly smooth. If it doesn't, gonna have to look deeper.

 

I replaced mine a few months ago w identicle off same type truck an it was under 300 an not to tough .I wont do a replacement of inside pinion an all ,so that was much easier.




Insides

working great still ,just match up the VIN spects.

mine was that inside pinion bearing ,an it was howling depending on speed.But no oil in it may have done internal damage you cant see .
Pull the cover an look for shavings an look at the gears too.

But you had humming too ,like me, ,the faster the louder .. -- i bet its the pinion bearings like mine [ cant see em without taking it all apart] an its 3 times longer ,with detail rebuild ,than another rear end ..[ pretty easy as long as you tighten to specs ]

 

Yeah on mine the faster I go the louder the whine/hum, I think my rear end is shot but I'll of course check wheel bearings first..the oil in my Dif looks new, so I suspect previous owner ran It low, put new oil in, problem didn't go away, sold it...luckily I got it super cheap so I'm not complaining

 

Yep ill bet your front pinion in diff is shot.. Jack it up safely like i did ,an have someone listen,[as you give it gas] , near the front of differential ,an also out at brake areas also as it hums .hopefully you can hear which area its coming from .But it may require a load or weight which makes it difficult..
.if you dont hear it when off ground, remove diff cover an look to see if any metal is sitting in bottom from low fluid damage ,if ok ,pull the wheel bearing seals an look at bearings,if good ur likely toast at pinion or inner gear area.

i pulled inner out too an still didnt see what i was looking for at pinion ,but it showed other bearing an all .