I'd try e-prize first. They were the administrators of that sweep. Did you save any of the correspondence that came with your card? I contacted them at fulfillment@eprizefulfillment.com. Just tell them which sweep it was (was it the Payday Payoff one?) and what the problem you are having is. They may need the card number.
~~~~~~~
Okay, I want to add that since I wrote this I got my own 7-Eleven card win in the mail. Checked the balance online first, and it showed $20. Went to the 7-Eleven, picked up some treats for my kids and at the checkout was told "This card is expired." I pointed out on the back of the card the bold lettering "THIS CARD DOES NOT EXPIRE" and told the clerk that I had confirmed the $20 balance right before I came to the store. No luck, so I figured it was a new clerk so drove 2 miles to the next 7-eleven. Same story, but this clerk told me I could use the store phone to call the1-800 number on the back of the card. I did, gave them the card # and was told "This card is expired" -- pointed out all of the above and the man said "Ok, you have a $20 balance, and this card does not expire. You should have no problem. If you do, call from the store" I explained that I WAS calling from the store, and WAS having a problem. He said "You won't have a problem now" and hung up. The clerk tried again, and same story. "Card expired." By this time there was a line of people waiting, and I was pretty upset. I told the clerk "I'm going to go be pissed somewhere else. Thank you" and left. I'll have to try again when its not 104 degrees outside, and I'm not too crabby, hehe.