It is a good sign that the scooter works with the battery charger connected to the scooter. To me it sounds to me like either power from the battery pack is not making it to the controller due to a wiring harness or connector issue, or that one of the batteries is defective.
The first step I would take is to make sure that the battery wiring harness terminals are firmly connected to the battery terminals by pulling on the connectors and making sure that none of them are too easy to pull off. Then I would check the condition of the wire connector that is between the battery pack wiring harness and the main wiring harness - sometimes this connector fails and does not transmit power from the battery pack harness to the main harness. This connector should not show any signs of overheating and its terminals should be shiny and not look like they have been overheated.
Next I would load test the batteries, or have them load tested at a local battery store. I know that the batteries are new, however some new batteries are defective so they could be the problem.
If these steps above do not solve the problem then with a multimeter I would test the Voltage of the battery pack at the battery pack wiring harness connector to make sure that there is not a break in one of its wires, and replace it if necessary. Following these steps should solve the problem. However if the problem still exists then please let me know and we will take it from there.
My friend gave me her scooter. She said she had it for like 4 years. She said the battery might need to replaced. I replaced the battery,which cost me $40. I charged everything up. I tried to run it and still does not work. I bought a new charger,which I bought for $10. Tried to charge it again. It still does not run. Any suggestions? You can hear the motor run when you have it on the charger and it putts along,while on the charger,but it does nothing while off the charger. It is a IZip 500. I am not sure why it is not holding the charge or whatever it maybe causing. Please help me. I hate to waste $50 and my wife need the scooter to get around.