From the MA website:
Q: I lost my registration code, can you resend it to me?
A: Unfortunately, we are not able to respond to requests to retrieve lost serials. Your options are to find the original payment confirmation and forward to support@maximusarcade.com OR purchase another license. (And this time keep it safe, use Evernote or similar to store the information)
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Most likely went through paypal, maybe check to see if you can find the transaction number from there.