First, go to Autozone to check if any code. Often automatic transmission problems do not trigure the check engine light(hope the autozone code reader is big enough to read manufacturer's specific code).
If the code shows park/neutral position switch malfunction, you may be able to replace it DIY.
If shows a valve or valves malfunction, basically you are likely in bad luck and need a transmission; unless you check and absolutely sure the valve the code refers to is malfunction.To check the valve, need to open the tranny and know the position of the relavant valve. It is a little too complicated for casual DITer.
My I suggest that you go to a Dodge dealer and let them to diagnose the problem? They may charge the diagnostic fee, but with their equipment, the diagnose is more reliable.