To check the resistance, just turn your meter to ohms, looks like a horse shoe, and put the black test lead on one wire and the red test lead on the other wire. Polarity doesn't matter. I would say since your solenoid doesn't spring return either direction, its toast. The spring may have come disconnected, or failed all together.
Here is a decent explanation with pics...
http://mechatronics.mech.northwester...solenoids.html