As Ian states you have two (2) items here; a relay under the tank that simultaneously cuts out the headlight and engages the solenoid AND the solenoid which engages the starter motor. You've apparently already replaced the solenoid, now you have to remove the tank and check the relay. It's on the right side of the backbone next to the indicator flasher (and the driving light relay if you have a light bar). The rubber keepers on those relays aren't real sturdy and that assembly may have slipped making it vulnerable to water intrusion and subsequent corrosion.
