This happened to me once with an eMachine; I called tech support and they gave me the number right over the phone, perhaps Packard Bell can do the same thing.
NOW I write all numbers right on the CD's with a permanent marker as soon as I get them!
You could have gotten the number from your registry before you reformatted, but it's too late for that now. The only things I know of that you can do now are either find your code or get it from Packard Bell (or buy another one).