maread01. Are you thinking that Adobe stores all your books somewhere in it's cloud, and expecting that when you register a new machine it will automatically access your books?
Many services work like that, but the Adobe DRM system does not. All the correct AdobeID does to to make sure that if you have a copy of a book registered to that ID, you can read the copy. It is your responsibility to keep a safe copy somewhere.
If you can get the old files off the broken comupter, you will be able to read them on the new computer registered with the same ID. As Jeff says, if you don't have such a copy, the only thing you can do is to try to persuade the original seller to let you download again. Good luck.