I had a problem with my 96 LX that did the same thing. What had happened was Best Buy buried the factory radio in the dash and it pinched and or shorted a wire and burned up the voltage regulator in the alt. and caused it to over charge. It blew the alternator and did the same thing that you are describing. The speedo is electronically controled so if the the electronics get messed up, it will do that.
The story has a happy ending though. Best Buy forked over $800 to get my car fixed.