Got a decent quality volt/ohm meter??
this is Not rocket science... either bad battery, even if New!!! or faulty charging system..
Unless someone been "Fixing it"... Then, Who knows..

 

May be time for a solenoid rebuild kit. Easy to check, pull the cover. My guess is the contacts are fried.

 

Ignition switch on, I get the same voltage reading at the green wire location on the solenoid with the run/stop switch in both positions. No drop when the start switch is engaged (one click).

 

The run/stop switch simply energizes the "start" button and ignition. There should be no voltage on the green wire unless the kill switch is on "run" and the "start" button is pressed.

If it starts with a jumper, battery to solenoid - with the switch and run/stop on (forget start button) and starter relay unplugged, jump across the #30 and #87 position of the relay harness plug. If it turns over, replace the starter relay.

 

Jumped 30-87 on the starter relay plug and it runs. Heading out to get a relay. Hoping to get lucky and that’s the only problem. Great tip for someone trying to diagnose this problem!

 

Good deal.
Before you call it done - when you get the relay installed and starting properly, put your volt meter on the battery. When starting, it will drop to about 9.5 - 10.5 and when running it should raise to 13+ volts within a few seconds and climb to near 14 volts within 30 seconds or so, depending on the charge of the battery.

You clearly had a battery issue at the start of this but insuring the charging system it doing what it should might save a disappointment later.