Verified answer

Nope, the 2 have nothing to do with each other. Fuel cutoff switch will only keep the fuel pump from running, the starter should work perfectly fine, if not you might need a new solenoid or starter.

The fuel cut off switch is what it is , It cuts off the gas not the starter, If the cut off switch is defective replace it and go from there, Remember it only cuts off the gas to motor. good luck

keith is right, if the fuel cutoff switch is bad the car will not run because the fuel pump won't turn on, but it will still turn over just fine.

here's a link to them on ebay.