Here is my understanding of what happened before and after the introduction of Magic Your Way tickets and how old tickets are applied.
*Before* MYW tickets, unused days never expired. If you had an old ticket with a couple of unused days left, you could handle it one of two ways. You could simply use the days as they existed on the ticket, trading that paper ticket in for a mag-stripe ticket as necessary.
Or, you could have Disney calculate the dollar-value of the *remaining* days, based on the original purchase price, and then apply that amount toward a brand-new ticket purchase. So if you have a 4-day ticket that was purchased for $97, and you have one day left on it, you'd get a credit of $24.25 toward your new ticket purchase. If the ticket came with extra "minor park" admissions, those were *not* factored into the value calculation.
Before MYW, when each additonal day was about the same price, those admission days were much more valuable as admissions, rather than a credit, especially on very old tickets.
*After* the introduction of MYW tickets, I believe they stopped issuing dollar-value credits for those old tickets, and simply forced them to be used as they already existed. (So what the OP has is essentially a 1-day park hopper ticket).
And even if they did allow you to upgrade with a dollar-value, as stated above you'd only get about $24 credit for the single unused day. So it's much more valuable to save it as a 1-day hopper.
Lastly, when you trade in the old paper ticket to be a mag-stripe ticket, the ticket is locked into what it is. They're not issuing you a brand-new 1-day MYW hopper ticket. They're encoding a special ticket with the exact entitlements as the old one, and thus you can't add days to it.
At least that's my understanding of things.
EDIT:
AHA! I knew I'd read a long Ticket FAQ somewhere... It's over on the DIS, a very long FAQ written by a Cast Member who deals with tickets as part of his job. Here's the specific part about upgrading pre-MYW tickets:
http://www.disboards.com/showpost.php?p=18654397&postcount=8
(Long story short: partially-used pre-MYW tickets can only be used as they currently exist. There is no upgrading or trading in. Only totally-unused tickets can be traded in for a credit of the original purchase price, but that's not usually the most economical choice)
As for not using the tickets in 21 years, wow... The closest I come to that are two as-yet-unused DisneyQuest tickets from late 2004.
-Rob
