Sounds to me like there is a lens problem if the batteries are both good and the camera cannot boot up and the camera will need to be serviced.
Are you certain about the condition of those batteries and charger? They may look like they've charged fully but when a large drain is put on them like the camera starting up they go dead immediately. I've had that happen to me before with a different model Canon camera. I tried a new Canon battery and the camera worked fine.
It could also be the internal DC to DC power supply too but the cheapest thing to try first would be a new battery and or charger. Get it from a place with a liberal return policy like Amazon or local even as long as you can return it.
