If you must lift the "bubble" to turn it off, it sounds like a bad switch. If you aren't sure and want to see if you can give it some life, shake it real hard for a bit (with the pump unplugged), then see if it works for a day or so. But I would get a new switch.
Be sure you find one that is rated for the HP of the pump, and is a "pump down" or "normally open" model. They are available at HD and quality pluming supply places.
I recommed the kind that are separate from the pump and that have a special plug that you plug into the wall and has a place to plug the pump in "piggyback".
The backflow valve should not affect the switch unless it is not working (stuck shut). If the pump discharges water when it runs, then the check valve is not affecting the pump or switch.