I am currently running Windows 7 32bit. I have both the Cisco VPN client and the Shrew Soft VPN client, both work as expected. The only problem is that I lose connection with the internet so I cannot browse Google, etc.
It is standard practice to route ALL of your traffic over a VPN connection while connected.
There is often a setting within the client to only send traffic destined for that particular network over the VPN connection, but this is called split-tunelling, and is considered a security risk. The problem is that an attacker could gain access to your computer over your regular connection (virus/backdoor/etc), and they would now have access to your corporate network via the VPN - effectively bypassing any security your corporate network has put in place.
The Cisco VPN Client has an option for "Split Tunneling".
This allows you to see your network and the connected VPN Network at the same time.
What sounds like is happening is when you connect to the VPN Host they do not have this option enabled, therefore you use their resources for everything. If you want to surf the web it would be off their connection, ISP, IP Addresses etc. If they have locked this down you would not be able to do so.
I had a similar problem where I could not see my network printer at home once I VPN'd in until split tunneling was enabled.