I think you have two problems. The engine continuing to run is probably related to the addition of the voltmeter and may be as simple as a miswire allowing current to continue to flow to the ignition when the switch is off. That is why I asked exactly how did you wire the voltmeter in, both sides. The other problem could be the switch, but also could be your battery cable condition and grounds. Just use an old screwdriver to short the big wire on the solenoid to the start lug on the solenoid. If the engine cranks well, the switch may be bad and the battery cables should be OK.
