Small Engine Troubleshooting Problems? Ask a Mechanic Now.
This sounds like you either have a bad battery, or you have your batteries turned off.
If you are getting 13.7V to the starter solenoid, it is because you have the unit plugged in, and are getting converter voltage.
But the converter can not provide enough amperage to run that starter. You will burn up the converter if you keep trying.,
Make sure your house batteries are turned on at your master switch.
If they are turned on, you will need to take the batteries in to have them load tested. Do not rely on a voltmeter to tell you if the batteries are good or not. They must be load tested.