Dodge Daytona 93

I have a Dodge Daytona that is driving me crazy! The situation is that as I am coasting or driving at low speeds (35mph or lower) the car motor will fail. I initially thought that it could be attributed to the fuel filter or pump but those are fine and have been replaced. The only other clue that I have is that the numbers on the clock and radio will go out-could it be a bad connector problem on the battery? Does it need to be rewired? The battery is only a year old.