1998 Honda Civic Speedometer Not Working

In the past few weeks, the speedometer and odometer have nearly stopped working. They work intermittently, and when the speedometer works, the odometer works as well. When they aren't working, the speedometer shows about 20 mph. When going a very slow speed, it jumps between 15 and 25 mph, and then "averages" at about 20 mph at higher speeds. When starting the car, it jumps up to either 15 or 25 mph. Occasionally, I can "jar" it into working by hitting the reset on the trip odometer, but this usually doesn't work. I was told that it was most likely the vehicle speed sensor. However, I tried a brand new one, and it did not fix the problem. What else could it be, and if so, how would I go about fixing it?