You are trying to browse network resources while connected. However, the way that you are going about it will not work unless your home computer is setup as a client on the network. For example, if you were to take your office computer home, install a vpn client and then connect to your company, you would probably see your domain and resources.
What you need to do is map the network drives that you need access to from your home PC when you are connected via VPN.
Simply open MY Computer, click on the tools menu, select Map Network Drive, select a driver letter and type the path the the network resource.
Eg. if you had a shared folder on a server at work that you needed access to you would do the following.
Suppose the server name is RIG and the shared folder is Public, the path you would enter when mapping the drive would be: \\RIG\Public
After you hit Finish you will be asked for your username and password again to make the connection.