Gas gauge on 2003 Buick Park Avenue

The gas gauge doesn't work. It gives no indication at all.

Asked by for the 2003 Buick Park Avenue
Fist thing I would do is throw a bottle of Chevron Techron Concentrate into the fuel tank and drive it. The fuel level sensor in the tank can get corroded and dirty from the contaminants in the fuel and this additive will clean the sensor, and possibly fix the problem. It's about $15.00, so an easy inexpensive attempt. Make sure it's the Concentrate Plus, it's the only one I know of that cleans these deposits.