Something a bit kerflukey here. Originally you said that when you pressed the starter button, the lights dimmed and the starter motor did nothing. This indicates a heavy current draw (the solenoid coil). Nothing happened re: starter motor. Indicates that the solenoid did not engage providing high current to the starter motor. If your starter switch contacts measure > 1 megohm, there is no way the lights would have dimmed. Also, it indicates that the grounds could not have been interrupted.
Why do you now think that the solenoid is toast? Did it heat up? Did you hear the armature move?
The solenoid doesn't care what the polarity is. Nor would I have connected it directly to a battery for any length of time. It is designed for short powered intervals.
If you did not experience excessive heating, then the armature is more than likely stuck.