continuity means you lose resistance when you turn the switch on, because turning the switch completes the circuit. Put your multimeter on ohms, like 10k or something, and it should say NC (no continuity) or 1 or a really high number when you measure across the switch with it off. With it on it should read a low number, when you touch the two voltmeter leads together it should read 0, or "no resistance"
You already said the test light doesn't show voltage at the wire going into the solenoid when you turn the switch, so now check if the switch is getting power. If it is, you probably got another bad switch.
edit: dam you wolverton
and robert you are using a relay to activate the solenoid because the solenoid needs more than the 2 or so amps that old corroded wiring and switch can give it, but the small relay can activate on those 2 amps and give the solenoid 40 amps