How can I reconnect home ethernet that has been terminated outside?
To activate it you will need to create a network with a hub, router or switch. If you are adding broadband Internet access, you will need a broadband router which will share Internet access with the network. 

Only thing is, the Ethernet cables should be terminated inside the house (unless you are planning to share your network outside the house). Home networking equipment is for indoor use only. This solves the issue with not having an electrical outlet.