Is your static ip set in the local area connection properties? or is it obtained from the router, but the router makes sure you always get the same one? Coz if you already have the local area connection properties modified, why not just set the dns servers to what you want (directly below the ip settings in the local area connection properties dialog), or do you not have admin rights or something on the computer?
What is the model number of the router? perhaps I can point you in the direction of how to set the dns servers from within it, that is of course if your computer is retreiving its 'static' ip from the router