Ruthie,
I know it’s been a few months, but I was wondering if you have fixed the speedometer yet?
I had the exact same problem with my 96 Neon, and it eventually spread to all of the other instruments in the cluster. I finally had my mechanic fix it while he was working on something else, and it wasn’t that expensive to fix. However, this is a known problem in ALL first generation Neons, so don’t waste your money on a replacement cluster. If you still feel up to doing it yourself, I would recommend getting a battery-powered soldering iron from Radio Shack. They don’t get too hot, so the risk of damaging the circuit board is reduced.
Good luck.
Joseph