Although it could be a failed speed sensor (which would cause your check engine light to come on as well), on a Neon it is most likely a failed printed circuit board in teh dash. They had a LOT of problems with these, and i believe there is a revised design part to correct the problem.
If you can remove teh instrument cluster fromt eh dash, you will see a flexible plastic printed circuit assembly that is all of teh dash wiring in one part. It is very easy to replace once the cluster is out of teh car. Replace it wioth a NEW one, not used; or you may have the same problem all over again.