try replacing the output speed sensor on the transmission housing. Just a small part (about $30 at auto parts stores), it screws into the transmission housing and sends a signal to the computer. Without this signal, computer cannot decide what to do with speedometer and cannot shift transmission properly. I replaced one on my daughter's 1999 Plymouth Breeze, with the same engine as the Neon. She had the exact symptoms you do, and it solved them all.
Sounds like the speed sensor is bad.
The speed sensor sends a signal to the speedometer to show the correct speed and it sends a signal to the transmission telling when to shift. If the speed sensor is bad the speedometer will not work and the transmission will not shift correctly.
You need to have the trans computer checked for codes. There will be a code that will lead to what is causing the no shift.
It could, vehicle speed is very important in shift scheduals
Output speed sensor is bad. Changed already
That's how you're taught - use the tach to determine when to shift, and the speedometer for recovery speed if you lose a gear. After a while, you get to the point where you know when to shift by the sound of the motor.
There are fuses in the cabin and also under the hood. You may need to actually pull each fuse to inspect it.
Check shift sensor
How do you change shift cylinoid on 1998 dodge Durango
TCM Malfunction, And/Or Speedometer Sensor Malfunction.
If your speedometer isn't working then that gear needs replaced before it'll shift
Most likey the speedometer gear in the transmission. It sends a signal to inform the computer of speed so it can shift properly. Check to make sure the electrical connector is firmly attached. The speedometer gear may require replacement, but it's important to be sure it's not a wiring problem first.