2004 dodge 2500 Cumming auto trans shifts good but not into 4th and up
If there are no faults detected by the PCM look closely at the PCM/TCM inputs for a problem. For example if the park/neutral safety switch malfunctions the computer will not allow overdrive to engage.
Not sure if the auto has shift solenoid, I have a 6 speed but I’ve had another car where the shift solenoid was sticking, I replaced it and solved the issue. Some are located within the transmission, some are accessible by just dropping the pan.
There are a lot of transmissions shops that will do a free road diagnostic test. I’d stay away from chains, smaller shops can’t afford crappy service as much as a big chain can or they’d go out of business. Shop around, do research on a good shop in your area.