I had the same problem a few months ago. It went away after I had the pressure control solenoid replaced. The humming is the sound of a bad solenoid begging you to replace it -- if you don't, your overdrive will self-destruct and you'll most likely need a rebuild.
Do a search here or in a few of the Buick forums(LeSabre, Century, etc...) for "PCS" or "Pressure Control Solenoid" and you'll find a million other cases of this exact problem.
After the intake manifold gaskets, the PCS seems to be the second most common "major" problem with these cars.
Also, this can usually be fixed cheaply($300 -$400) without dropping the tranny. However, you'll probably be better off if you spend the extra cash and have the tranny pulled out and other potentially problematic parts replaced before they get a chance to cause you grief. Aside from the PCS, the TCC will go on you eventually, along with one or two other PCS-related parts that I don't remember the name of right now.
These trasmissions are garbage, so it's best to pull them out once and get it over with.