Tom, just went thru the same leak problems with my Sprinter skylight (see my related posts) and my teardrop windows over the cab. I just finished having my skylight fixed (I hope) by pulling the whole unit and putting a good and adequate seal underneath the unit where it sits on top of the roof fiberglass. The factory seal was useless and poorly installed. I sealed the windows around the outside edge about a year ago and no problems since. Keep and eye on all your windows since every one of mine leaked at one time or another in the first year of ownership.
My furnace did the same thing last winter. If you are comfortable, pull the interior cowling off of the AC unit and look for a loose wire that controls the furnace (yes it is in the AC unit). Mine was an easy reattachment and solved the problem. The RV tech who told me about this says it is a very common issue in these Dometic systems.
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