I just had this problem on an 04 Grand Prix and it landed up being just the blower motor, resistor was fine.
I really wish I researched the fix a couple years ago when my parents had the problem the first time. I just put the rubber strip back on thinking a lube shop had knocked it off putting in the cabin filter.
I called the dealership parts department and gave them the part # from the TSB from Feb05, and they said the part # changed to:
plenum water deflector (Part# 15794785)
So it is in the system even if you give them the old TSB part #.
That is the correct part #. Why they even have the old part # for the rubber strip is beyond me.