Edward's on the right track, but isn't quite correct about some of the details.
From what I've heard, there are two ways that a Guest Relations CM can upgrade an totally unused ticket. One way gives you a credit for what you actually paid for the ticket (meaning you don't get credit for any ticket price increases since you bought the ticket), the other gives you the current gate-price for the ticket. Either way, that amount is then put as credit toward the new ticket.
If you've *used* the ticket to enter a park, even if it's just once, as long as you're within the 14-day window from first use, the system can then only issue you a credit for the current gate-price for the ticket. It's simply a quirk of the system. (FYI, the No Expiration option does nothing to extend the available window to upgrade a ticket. It's 14 days no matter what)
As a side note, this process also applies to tickets purchased at a discount from an authorized ticket reseller like Undercover Tourist. One way of upgrading would only give you credit for the amount the *reseller* paid Disney for the ticket (i.e. the amount of money that Disney got for it) in which you'd lose the amount that the reseller marked up the ticket for profit; or you could enter the park first and then get more than what you paid for the ticket...
Unfortunately, the OP has stumbled into one of the few situations where there may be a problem, and they may get screwed in the transaction. The ticket they have is worth MORE than the price of an Annual Pass. As far as I know, they'll still exchange your ticket for an AP. *But* you may end up forfeiting the remaining balance. I'm 99% sure that there are no refunds in this instance. Plus, because ticket upgrades are on a 1-to-1 basis, you can't apply that excess balance toward another ticket.
So, you need to figure out what is a better use for that ticket... What's the amount of money you'd lose on the transaction? Is the trade worth it to you? Or is it better for you to outright buy a new AP, and then hold onto that ticket for the future so you can use it a few days at a time after the AP has expired? Who knows, perhaps you'll find that Guest Relations can work some magic and give you the balance on a gift card or something, kind of like a "merchandise credit" at a store...
Oh, and after you've gone to Guest Relations and asked, make sure to come back and let us know. It'd be good info to file away for future knowledge.
-Rob