How to change a static assigned IP?

[Anima]

This computer and IP is being recognized by websites with stored data for this IP. This is recognized even after accessing these sites with proxies, an anonymizer (smarthide.de) and a secure tunnel (GoTrusted Secure Tunnel).

But somehow, the sites are still recognizing the computer and the IP, probably seeing through the proxy or tunnel to see the static IP of the computer.

Is there any way to change the IP of the computer, when it is a static one being assigned by the server? I don't think I have access to the router (is that the wireless box?), since it is a wireless network in a building. Without asking the company to do it, can I have the IP changed?

Can I change the identification of the computer, that they are using to assign the same IP to?