From your post it's difficult to pin point a problem. You said that with the charger on the lights would work, but when you installed a new battery, no lights. This would tell me that either you have a bad battery or a loose connection. It could also be one of the safety switches. Are you sure the PTO switch is off? Does the solenoid click when you turn the key? Have you tried to jump the two large terminals on the solenoid to see if the starter works? Please check these and post back, so we have a starting point to help you.