2001 Dodge Ram Whining/Warbling/Humming When coasting or no

I have a 2001 Dodge RAM 1500 4x4 extended cab with a peculiar issue. My wife was driving it when she heard a loud "pop". After the pop the truck started making what sounds like a warbling/humming type of noise when going over about 20 mph (may actually do it going slower now as it seemed to gradually happen more often before I took it into the shop) and let off the gas. No noise when accelerating but when coasting in neutral or when letting off the gas. I took it in and the third member (?? The large gear with the clutch plates) of the rear differential was replaced with a new one. Didn't work. All the bearings in the differential were replaced, didn't work. The transmission was looked at and I'm told it's ok. They opened the transfer case and everything appears fine. The mechanic is at a loss right now and is about to give up (after charging me at least $2k or more). Do any of you have any ideas on what the problem could be? Your help is greatly appreciated! Thanks, Richard
(if your info helps solve the problem I will give you a donation)