It will only start in neutral while on the sidestand. If the bike does not stall when you put it into gear then the problem is not the side stand switch. The earth from the side stand switch is needed to keep the Ignitor alive when riding.
I would check the connections at the starter cut out relay under the left panel for corrosion.
The 600 usually does not require choke to start when cold just open the throttle a little, then if need give it some choke. Change the plugs and balance/synch the carburetors, this will help to sort the starting issues.