There is probabley more than one problem.
The petcock may be leaking anf the floats may be sticking.
The floats have to be sticking, they hold the flow of gas back even with the petcock open.
I'm sure you have seen the great miracles of Seafoam talked about on hear, Easer to do than pulling the carbs.
If it doesn't work then you may have to pull the carbs anyway but it is a good start.
Check the plugs make sure they are not fouled, if it got that flooded they probabley are. Get a new batt and keep a charger on it if you are trying to start it alot.
Do not try and start for to long the starter will not last long if you hold it down to long, 10 seconds is as long as you want to try.
Chad Falstad "Hawk"
2011 HD Ultra Classic "angel"
2001 Nomad 1500 Sold March 2012
2001 VN 750 "Sold June with 2008 with 21,000""Serinity"