2005 PT Cruiser Vibration

I recently purchased a used '05 PT Cruiser (non-turbo). Generally
speaking, the car is wonderful with one small exception. I frequently
get a vibration through the entire car when accelerating to or from 20
MPH. Below 20 and above 30, the ride is smooth.

The car has an automatic transmission, but the vibration very much
resembles the same kind that you get when you are trying to accelerate
while in the wrong gear on a manual transmission. It doesn't happen
every time I accelerate and it is VERY pronounced when I am coasting
through a parking lot at 20 MPH and press down on the gas. I took the
car in for service and the dealer replaced the two front tires, did an
alignment, and balanced all the wheels. I still get the vibration.

I realize that the dealership should (and eventually, will) fix this
problem, but I need to steer them in the right direction. Can anyone
give me any ideas as to what might be causing the problem?

 

bent or failed axle shaft