If I'm deciphering what you wrote correctly, I'm guessing your float isn't rising to trigger the pump? Can you manually move the float up to trigger the pump? Check the float for holes that allow it to fill with water, and repair it. If the switch is bad, you can buy replacements on the internet it seems (quick Google search). I would run down to your local hardware store and just buy a replacement pump, which you should really have on hand anyway.
