If you go to the disney site (linked above) and follow the steps to clicking on the Dining Reservations, they might show up there. It depends on if you were logged into your account (and possibly close enough to the date of the new system) when you started the ADRs.
If they are not there, you're going to have to call to get the confirmation numbers and other information as there is no other way to do it online. After you have the confirmation numbers, you can use the box that asks about retrieving to pull them up.