Now let's see what could be wrong.
--If the pump fails, then water will overflow from the tank.This will be evident if the tank is full. You don't always have to change the pump, which is about $50-80. It is likely caused by the switch which operates with a little float. This switch can be ordered at appliance part stores. To check whether the switch works properly, you just open the cover and pull the float up and down to see if the pump motor runs.
--If it's not the pump, you probably have a pipe that is not properly sealed(check all the junctions). You may have to turn off the furnace for a few hours to let the pipe dry out, and then apply plumbing sealant.