After you've checked the float switch for operation, check to see if the pump operates from the panel. If it won't kick on at all check and clean the ground connection. If it operates from the panel but not by he float, check and clean the connection from the float to the battery.
Corrosion in wiring connections cause 99% of these issues and cost next to nothing beyond labor to repair. If corrosion is the culprit you ma find that it has crept under the wires jacket turning the wire black. Cutting it back until you find clean wire will be required and splicing in new wire is the cure.
Good luck with it.
Mike.