Yes you can sue. Sounds like the perfect case for small claims court. Search on line for instructions on how to do this in your area.
I am not your lawyer and an answer on AVVO is not intended as legal advice but is provided for general informational purposes only. If you desire legal advice, please consult a lawyer and form an attorney client relationship.
You potentially have a case agains the seller for making representations and warranties in an ad about a product that turned out to be false. Did you sign any paperwork that made this an "as is" sale or disclaimed any warranties?
Before resorting to a lawsuit I suggest you try to work things out with the seller. Perhaps the xbox is under a manufactures warranty and the seller will give you some money back for the inconvenience of having the xbox fixed under a warranty.
If you are unable to work things out with the seller and you feel that your only resort is to file suit, I suggest you file suit in small claims court as this could be the most cost effective method of recovery. Be prepared to have a copy of the ad as well as any email correspondence between you and the seller to support your case.
The above constitutes general information only and it neither intended to be construed as legal advice nor create an attorney client relationship.