Using a multimeter on the solenoid (without power applied, and power applied), would have proven the solenoid bad. Many switches, sensors, etc..can quickly be diagnosed by using the multimeter and checking resistance. Last night I tested an ABS rear brake sensor on my Explorer by using the multimeter to compare the old sensor and new prior to installation. You can still bypass with the wire and verify, but the multmeter can save a lot of time.. Just thinking out loud...