@hacsat, About a week after i purchased my 3790T had same problem, it is true that some of the units have had battery problems and checked with garmin to seen if my unit had the serial number corresponds with problem, but my unit was newer so no issue there.
What i did is connected the unit to the car cradle for about 30min on charge and removed unite, I pressed and HELD the power button on until it turned on, I recall it was bout 30second or more, so i would try and hold the power button on hold it as you have nothing to loose but you unit for a month.