The airbag sensor and weight detection system are probably under the passenger seat. Even if the floor isn't that wet, the wiring could've gotten damp. Once everything's totally dry, try gently unplugging and replugging the connectors.
If you're comfortable with electrical stuff, you could try just connecting the wires where the switch goes to see if the motor runs. That'll tell you if the switch is the culprit before you spend money on a new one.