missing serial number for elements

Hi, I need to move my Elements to a replacement computer but have an odd problem.  I use a legal copy of Elements which I purchased as a teacher edition and had a serial number for.  Unfortunately, the email with my number has been lost somehow. I have gone into my Adobe account, looked for my products/orders, and there is no record of my photoshop elements listed, only my lightroom purchase shows which I also purchased around that same time (winter 2015).  I have been on Adobe chat where the agent told me to basically look in all the places I already listed in my opening chat statement or to locate my email - which I have also tried.  My last ditch hope before having to repurchase the software would be if I could locate it on my computer where the product is installed... is this possible? Is there any other place to look for the serial key to this software?  I am upset that I lost this serial key, which I had saved for this very reason, but lost somehow but also dont understand why Adobe has no record of my registered elements as like I said, is a legal copy which I paid for.  The only info I can find is in my "about Elements" under license it says "perpetual".  Any assistance would be greatly appreciated.

Andrea