I started having the same problem after I put the spare on. But that had nothing to do with the whiny noise coming from the engine.
One place couldn't duplicate the problem. Another checked the belts and decided it was the AWD system. The third (dealer) couldn't duplicate the problem, although I hear it no matter how fast/slow I drive or hot/rainy it is.
I finally got a diagnosis after taking it to a 2nd dealer:
The problem is the center bearing in the drive shaft under the vehicle. Unfortunately, the bearings are sold with the drive shaft. The drive shaft alone costs $600+. The mechanic at the last dealer said it works fine, it is just a noise I will have to tolerate if I don't want to replace the shaft.
I did find something on the internet regarding the drive shaft on 2004 endeavors. They were recalled b/c the bolts may be loose or missing. Recall ID # 04V314000. Call (800) 222-0037 to find out if your vehicle is one of these. I definitely am.