Voltage at the battery is 12vdc. Next I tested it at the solenoid with the key in the "on" position, and the voltage was 0. (I conducted the test with the key in the "on" position, not cranked over to the "start" position. Was this a mistake? It seems like I should have had someone hold it in the start position. Also, I tested across the two red battery leads, one goes from the battery to the solenoid and the other goes from the solenoid to the starter. Was this correct?)
I then cleaned the battery posts, the ground connection to the block, and the purple ignition wire connection to the key switch. No change, sometimes it starts, sometimes it doesn't. I am not sure what the purple ignition wire from the key connects to, so I couldn't clean that end. Where does it go?
Any other suggestions on where to look?