Sounds like a bad fuel pump. However, how much fuel is in the Winnie tank? The intake stick for generators sometimes only goes down to 1/2 tank, more often to 1/4 tank, to prevent the coach from running out of gas. So maybe it's not picking up fuel because it can't reach it?
The wire from the fuel pump should be energized with at least 10vdc during your generator cranking; test it with a voltmeter.
Fuel pumps can go bad with no notice or prior symptoms; often a ruptured rubber bladder inside. However, most genny pumps are not ordinary automotive fuel pumps (low psi on genny models). A Kohler dealer would be your next call for a rebuild kit or pump.
Last Brave 2004 34D