My mom went through something similar, but it wasnt a win. It was a check from an attorney that was handling a case for her. She moved to Florida. So she contacted Fedex and gave them permission to let me pick it up, after she sent them the requested information.
So its possible if you have a family member or trustworthy friend, that you can have them pick it up for you. Then perhaps she could fax it to you if it has a deadline or fedex it to you.
Just another route incase.
I mainly posted here so that I'd be updated when you post what you won. I hope it's something nice! Call the sponsor of the contest if they have a short deadline to get it extended.