buy a new battery and spark plugs
He already bought a new battery. New plugs may help, but for now, the old ones can be cleaned and regapped. Unless they are broken, in which case new plugs will definitely help.
Also make sure there is a spark to all 4
plugs. The Vulcan 750 will run with just one plug per cylinder firing, but it does not run well. Make sure there is gas in the float bowls, and that the carb float bowl vent is clear. If that stuff checks out, I'm almost certain the problem is with the carbs or choke.
I would start by removing, disassembling, and thoroughly cleaning the carbs. Make sure you get everything back right, and look for anything wrong while you have them apart, including with the choke assembly and cable. When you reinstall the carbs, make sure you get everything back in place properly, and have no air leaks. Removing and replacing the carbs is not a real easy job, but with time and patience, it is not that bad.
Also, try running it with the gas cap open, just in case the tank vent might be plugged up. This is a fairly common problem on bikes with the CA evap emissions crap on them. Jerry.