All activations used

I have been using Elements 9 for several years, initially installed on a PC which I replaced after a few years.  The hard drive of that PC was wiped. I installed PSE 9 on my new PC and used it for a number of years. I recently reset that PC to factory settings (without first deactivating PSE 9 - in hindsight clearly a mistake on my part). Now I cannot use PSE 9 because Adobe's records show that it is already activated on two computers. It is not currently activated on any computers.  I contacted Adobe help via chat.  90 minutes later the result was that they couldn't help.  On multiple occasions they said I must first deactivate it from one of the PCs, despite being told that that would be impossible. Their suggestion was to contact the forum for help with a "work-around".  I fail to see what sort of work-around could possibly allow me to reactivate PSE 9.  However I am happy to be proven wrong if someone here can help.