I've been struggling over the past year with connecting to off-network sites when firing up a connection to a client's network via the Cisco VPN client. Once the connection was established I could get onto the client's network resource alright but could only get to a scant few outside websites. That's a little difficult when working on an intranet site for the client and needing to research something (which I am constantly doing).
This was only happening on my desktop machine. My laptop connected just fine. I logged both of them in at the same time and went through every conceivable setting for the Cisco VPN adapter, the physical network adapter it was piggy-backing on, and the VPN client itself. Vista Home is running on the desktop, Vista Business on the laptop. The only other difference was the network hardware itself -- wireless on the laptop, ethernet on the desktop.
That is, until I double checked the version numbers of the client -- 5.0.00.0340 on the laptop, 5.0.03.0530 on the desktop. I had upgraded the version on the desktop some time ago due to some weird bug with the VPN client in Vista where the client would work a few times and then absolutely refuse to connect afterwards, getting to the "securing communications channel..." phase before bailing out. The new version of the client fixed this problem, but also apparently fixed-up off-network connectivity.
After downgrading to the prior version of the client, voilà, I can get on their network and public websites at the same time.
The original bug can be worked around be resetting the Cisco VPN adapter in the network connections window. When disconnected, enable the connection by double clicking on it, then right-click on it and select diagnose. Select the reset option at bottom and it seems to fix itself.