If you see all the lights on the modem LED up and device are connected to home network without internet then you need to perform hard reset on the modem, after resetting the modem will go to default setup any custom settings will be removed so use the default network name and password to connect to your network. After resetting modem you no need to activate modem by your service provider if they confirmed that your modem is activated. please follow the steps mentioned on the below article to perform hard reset on the modem and to setup the modem on the GUI.

http://arris.force.com/consumers/articles/General_FAQs/SBG6700-AC-v8-6-x-Factory-Reset

http://arris.force.com/consumers/articles/General_FAQs/SBG6700-AC-Web-Manager-Access