This sounds like the Cisco firewall is blocking the RDP connection from the VPN to the LAN. Firewalls can be set up to have different rules for LAN to LAN traffic compared to VPN to LAN traffic. Admins often set up zones, similar to VLANS, inside the firewall. Each zone can have different rules for which ports are open and which packets are dropped. Most modern firewalls can identify a service and drop the packets based on the type of service.
For example, I was tired of the kids downloading movies on our public internet at work, so I configured the firewall to block all peer-to-peer protocols on the zone with the wireless connections. So peer-to-peer is still available for authenticated users on the LAN, but not to anonymous users on the WiFi. This is an example of granular rules for different zones.
Ask the person who contols the VPN/Firewall which ports are open, or maybe even do a port scan yourself. If you really want to make it work you could do something complicated to tunnel through the firewall over an allowed port using an allowed protocol. This is what LogMein does - the LogMein application tunnels over port 80 disguised as a web request. And it sends the traffic as a response to a request from the host behind the firewall, so it gets through.
But this really shouldn't be necessary. If you are trying to do legitimate work, just ask the person who controls the firewall how he/she wants you to make your connection.