Why can't I access the Internet when the device is on Battery?

When your device loses AC power, the LAN, Wi-Fi Interfaces, and TEL 2 are disabled to save battery power for TEL 1 functionality.  The battery is designed to last 8.5 hours when idle (no calls are made or received), and 4 hours when making or receiving calls. The purpose of the battery is to provide telephone service in case of a power outage.