My 01 Ram 1500 is in the shop right now for this very thing. My kickdown band was shot due to a lot of towing. I have 135,000 miles on the truck. I tried to adjust the band, but the lining of the band was completely gone. It would not shift out of 1st until around 4000 RPM unless I ran it up to around 2500 RPM and momentarily let off the accelerator. The repair will cost about $488 labor and $185 in parts. It is just normal wear and tear.
Governor pressure solenoid and switch $150.00
My 2001 Dodge Ram 1500 Sport 4x4 is doing the same thing, I ran a computer and my speed/pressure sensor seems to be out, I've heard its an external sensor, so it should be an easy fix. 2001 transmissions have had many problems like this. So good luck!