Try the following.

1. Right click on the My Network Places -> Properties
2. Select the VPN Connection (ex. VPNConnection) from the list, then click Properties
3. Make sure the Dial another connection first: is unchecked.
4. Then try your Internet connection.

If the above procedures are still not working, try this

1. Repeat the above procedures
2. 

   Select Networking Tab

3. Select Internet Protocol (TCP/IP) from the list view, then click Properties button
4. Another window will appears, click Advanced button
5. Uncheck the Use default gateway on remote network