If my internet service is interrupted by the service provider, can I still access the computers within my workgroup? We are several computers, all running Windows 7 Home, with a mixture of wired and wireless connections.
Of course yes. Internet is a global public network. Any home network is by itself a self contained private network.
If you are unable to see other computers on your home network, you may have chosen "Public" as your network type. If you choose your network type as "Home" and your computers are on a "Workgroup" (not a domain) you will see them in each others network automatically, no configuration required.