Useable Premiere Elements 11 Serial Number

Question

I bought Elements 11 and Premiere Elements 11 together last year from Amazon.com.  When I tried to start Premiere on my old computer, it was taking forever, so I started and registered Elements 11.  Because I bought them together in one box, I didn't realize I had to register Premiere Elements with a separate serial number.  Now, I have a better computer and want to use Premiere Elements on it.  I was able to recover my registered serial number for Elements 11, but while I have the disks, I can't find the original packaging with the serial number for Premiere Elements 11.
I realize it's my fault I misplaced the packaging.  It's also at least partly my fault that I didn't realize the two disks were separate and needed two serial numbers needed to register.  Still, Adobe support'a chat  is unwilling to help me register this legitimately purchased product that I can prove I bought because I bought it from Amazon, which they say isn't an authorized seller.
Do I have any other recourse to register and use this legitimately purchased product?
Thanks for any help.
Tom

Answer 1

Thanks to all of you who responded.  You should all work for Adobe because your customer relations skills are greater than those of the person I spoke to on chat about this issue.
Maybe I should have known, but i didn't have to know that I needed two serial numbers.  Both programs installed just fine.  I registered Elements the day I got it and established an Adobe ID and password.  I had a previous version of Elements and don't remember if I established the password at the time I registered my first or second version. 
Elements 11 ran very slowly on the old computer.  I tried to start Premiere Elements but it ran even more slowly than Elements did and since I had no videos to edit, I abandoned the process, thinking one registration was all I needed and that I could return to Premiere Elements when I had some time and some video to edit.  I didn't get to a registration screen on Premiere Elements and I figured one disk, one password.  Maybe I should have known, but I didn't and as  far as I got in the process, nothing explained it to me. 
Next, and clearly my mistake, I misplaced the packaage with serial number information on it.
That was a year ago.  This week, I got a new computer.  I installed both programs. Again, no problem.   I was able to recover the serial number for Elements 11 and register it on my new computer.  The only painful part of that process was how long it took to get on chat with a representative who was helpful.  Elements runs faster on my new computer, so I started Premiere Elements.  It also runs faster on this computer, so I got to the registration screen and tried to register it using the serial number I had just recovered.  Having reached the registration screen for Premiere Elements for the first time this week and tried to register it was when I discovered that I needed two serial numbers for one disk.
I'm trying not to disparage the second person I reached on chat, but he or she did suggest that I should return year-old software I've been using and no longer have the original package for to Amazon, since Amazon is not an authorized seller of Adobe products, and rebuy it from an authorized seller. Whether the person on chat was stupid, I can't say, but that answer certainly was.  They said they were unable to help me because Amazon is an unauthorized seller.  That does imply that I could be helped if I bought it from an authorized seller.  Does buying from an authorized seller make a difference?  If it does, how was I as a first-time customer supposed to know that it's bad to buy from the world's largest retailer?
Since chat person #2 implied the reason I couldn't be helped is that I bought from an unauthorized seller, that also implies I could be helped if I bought it from an authorized seller.  I have the disk (and the Mac disk too) and can prove I didn't pirate it or even buy it used, so I hoped someone could help me to register Premiere Elements now that I have a computer that will at least let me start it and can get to the point where I know it needs to be registered under a second serial number I once had, but can no longer locate.
All three of you are telling me no.  It makes me feel bad that there seems to be no way for me to recover from an error I made that I think was a reasonable error to make.  However, all three of you told me no without condescending and in a much nicer tone than chat person #2 and all three of you responded quickly, unlike Adobe chat.  So, I do feel good about coming here and thank all three of you for your time.