Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! I don't know it all, but maybe together we can get you a satisfactory answer!
Generator starts with battery only. What is the battery voltage when you try to start? Does it drop below 8 volts? If it does, battery or cables are fault.
Get a better charger that will keep battery voltage above 13 volts. 12 volts is just a surface charge and is not charging a 12 volt battery, input from charger has to be well above 12 volts to actually charge battery.