Due to Nokia 710 battery terminal damages it can not be power ON. So if Nokia Lumia 710 is dead or no getting power. it may can be due to battery terminal damages.
Nokia Lumia 710 Battery Connecter Ways Track Path
Nokia 710 Bsi Line Jumper
Nokia Lumia 710 Not Powering On Soolution
If you find some rust or carbon you can clean it with electronics cleaner. Apply hot air to make it dry.
In above diagram there are different color lines that are used in battery terminal. Check these tracks and parts if any of these links is missing apply jumpers as given in diagram above to repair battery terminals of Nokia Lumia 710.