VPN connection disconnects your Internet session

The solution

First you need to pull get to the screen that lists your Network and VPN connections.
The easiest way to do this in both XP and Vista is go to Control Panel --> Network Connections (In Vista there are several other ways to get to this same screen).
One you are there, right click on the troubled VPN connection and choose properties.
This will open up a new VPN Properties form with a title of "VPN CONNECTION NAME Properties".

On this form go to the Networking tab and highlight the Internet Protocol Version 4.
Click on the Properties button and this will open up a new form with the title "Internet Protocol Version 4 (TCP/IPV4) Properties".

Click on the Advanced button and this will open up yet another form with the title "Advanced TCP/IP Settings".

The default tab here should be "IP Settings" and there should be an on/off setting named "Use default gateway on remote network".
Un-check that setting and you should be able to use your VPN session, but now you should have an Internet connection at the same time.