You must establish a good connection to the solonoid else all further testing or measurements will be confusing or meaningless. If the connection is good then you must have an additional problem elsewhere. It is unusual for 2 things to fail at the same time. The most common failure of the OD is the relay located under/behind the glove compartment. Assume you have checked the fuse.

With key on is the arrow on dash on or off? Does it respond to the button?

The method you used to measure for 12V at the solonoid is a bit unconventional but it apparently helped find the bad connection. (I think you mean open circuit and not short circuit. Typically a short refers to when a bare wire, connector or some component carrying 12 volts touches the metal frame somewhere. This will usually blow a fuse.