gas gauge stuck on empty.

You probably need a fuel sensor. Usually comes with the fuel filter and are replaced together......hope this helps

It was stored for 11 years. Could it be a rusted or stuck float inside the gas tank?

definately. The fuel sender unit is in the top of the tank and they are prone to sticking. From the back seat of the car you need to remove the storage compartment on the parcel shelf. Once this out of the way you will see a plug in a large bolt looking thing. Using a pair of large sliding grips, undo this and remove the sender unit. Yes, its the long aluminium tube.

on my 2003 sl500 when I start the car it shows full when I know the tank is empty when I turn it off it marks empty like it should what could it be.

Likely the same problem as the original post, the fuel sender units in the R230 chassis (2003 sl) are basically a piece of foam on the end of a metal rod that's connected to some electrical gubbins and screwed into the petrol tank. Of course, because there's moving parts, there's a likelihood of failure at some point. A sender unit won't be cheap though I'm afraid, expect to pay between $300 and $400 USD if you're buying the part yourself. If you're anal about dealership stamps you can probably expect to pay twice that amount.