Why does one windshield wiper not work?

@packergirl73 since one side works and the other one does not, this will be an wiper linkage issue. First you want to check to make sure that the wiper arm still connects properly to the linkage:

WIPER ARMS REMOVAL

(1) Place the wiper arm/blades in the PARK position and turn ignition OFF.

(2) Using a trim stick (special tool #C-4755) or equivalent (screwdriver;-), gently pry up on arm cap and remove.

(3) Remove the wiper arm retaining nut.

(4) Remove the arm from the pivot using a rocking motion while the arm is in an over/centered position.

(5) Clean metal splinters OFF the pivot shafts.

If that all looks good you'll have to check your linkage. Here is how to work on your wipers Dodge-Neon-Wipers.pdf