In order to establish a VPN connection, your computer must first establish an Internet connection. The VPN tunnel is then created after the VPN client is properly authenticated by a VPN server.
There are two basic types of tunnels: 1) Full tunnel, or 2) Split tunnel.
In a full tunnel all traffic goes through the tunnel. Typically, the VPN client can then access resources on the destination's network, which can include a campus webserver. In addition, if the destination also allows access to the Internet, the VPN client can gain access to the Internet this way as well.
A split tunnel allows the VPN client to send traffic through the tunnel, but also allow local traffic to be sent to the local network. If that local network has Internet access, then the VPN client can get to the Internet this way.
If you are unable to access the Internet outside of establishing a VPN tunnel, then there is something amiss your network configuration on the local network.