I had the same problem with my 95 accord. The speedo works sometimes and then doesn't work other times. It changes on and off even when I am driving. I took mine to the honda dealer and they did a test on it. It turned out to be a bad speed sensor which sets me back around 120 bucks installed by them. To know for sure they have to do a diagnostic test on it. They told me it could be two possible things that went bad and one of which was the speed sensor but therre is another part that can go bad to cause the same thing. And no check engine light will come on. The check engine light is mainly just for exhaust emission problems from what I have understood.