Does a 2003 Dodge Neon have a transmission modulator?

No neons do not have a modulator. The trans on this car is computer controlled and has a solenoid pack to control shifts. If it does not pull and you suspect it is a trans problem usually the solenoid pack, if one of the solenoids goes bad it will make the car go in to "limp mode" and it will start in second gear instead of first. It is a fairly common occurance for these solenoids to go bad. Hope this helps.  more