I have yet to come across VPN software I didn't hate but it's difficult to avoid using them. If you use Mac's Internet Connect to create a VPN connection and you can't seem to access Internet while VPN connection is open, it's because:
- Mac's built-in VPN client defaults to routing all network traffic through VPN.
- VPN network you connected to blocks outgoing traffic to Internet.
- Run Application > Internet Connect.app
- Select Connect > Options… menu command
- Uncheck "Send all traffic over VPN connection."