Can i sell a rusty old saxophone?

I'd like it if you still have it. 

You can try but that is not what people are looking for and what brand is it?  The question cannot be answered without knowing what brand it is. The only way it can have value if it is a rare one that someone might be looking for. You might try giving it away but it might not be worth the money to fix it up. 

Suppose you spend the money to get it fixed, but even so nobody buys it?

You're getting mixed opinions. I suggest you check with an instrument dealer, maybe a pawn dealer and see what they suggest.

First, write down all the info on it - brand, model, size (as alto, tenor, etc.  Take a couple of pix.  I am a professional flutist, and a few years ago a woman in Maine found a case in a barn, and took a pic of what she thought was as flute. I happened to be looking in ebay for cheap flutes  for my students to use just for marching, not to take their good one out. I FLIPPED when I saw it - and knew I could never win the bid.  She asked $100. OBO.  IT SOLD FOR THIRTY GRAND!!!!  I wrote her a nice note, telling her I was happy that her rare Boehm-Mendler (1855!!) had been found (in Maine???) - then I called my top flute dealer buddy in NYC. He yelled that I should have called him sooner - he would have paid 40, sold it for 50 grand!  So - you might own dirty plumbing - or a rare item.  DO YOUR RESEARCH!  Yahoo Groups has Saxophone lists - or call a GOOD Music store - or ask your band director in school.  Ya never know . . .

Even rusty, someone may buy it as a decorative item, but it wouldn't be worth much.  

As for repairing it, you should find out how much that would cost and how much the saxophone is worth IF you fixed it.  It might not be worth it.

Repair it first...

Someone may want it for an art project etc .  Sale it on eBay or something . 

Nope, because if it rusts, it's not brass but steel, so it's a piece of sh*t that sounds even worse than a piece of sh*t even on its best day.

You would need to fix it and that would probably cost more than you could sell it for.