ADE Not Authorizing ID on Replacement PC

I have had a copy of ADE on a PC authorized with my Adobe ID for quite a while. However, that PC recently failed and had to be replaced. I installed ADE on the new PC but can't authorize it - the message is that is has been used on too many devices. Well, that is currently not true as, if it was in fact used on any devices, most are all now gone leaving just the replacement PC and one Sony eReader. I need to authorize the replacement PC to access the many ebooks I have on the eReader. What do I do?