Dear Boris,
You probably mean that you installed the Cisco VPN client on the machines? There are two possible issues:
1: Your vpn is not set-up to allow simultaneous vpn- and internet access. This needs to be adjusted on the firewall. The feature is called split tunneling.
2: The built-in personal firewall in the vpn client is blocking your access. Simply deactivate it.
My guess is option 1, you will have to contact your system administrator to have this fixed. If you are the admin, check the pix command reference for the following command:
vpngroup group_name split-tunnel acl_name
Regards,
Leo