Did you (1) authorize ADE with an explicit AdobeID, or (2) did you run with the option something like 'authorize without ID'?
If (1), then authorize with that same ID on the reinstalled computer.
If (2), I am afraid you are probably stuck.
The Adobe system always runs with an ID. If you run 'without ID', if effectively generates an implicit/anonymous ID.
The anonymous ID is very limited in what you can do with it.
You can't use it with a second device. If you repair a broken computer and install ADE, it will generate a different anonymous ID.
When you buy/borrow a book, that sale/loan is associated with the ID you are using at the time, and the .epub/.pdf encyrpted for use by that ID.
So, in case (1) you can reestablish the original ID, and gain access to the book.
With (2), the book is associated with a dead anonymous ID. The ID cannot be regenerated, and the book cannot be read.
ADE does give warnings about the limitations of 'without ID', but those warnings are not nearly strong enough.
Thanks for the explanation. I re-installed ADE on the same pc but I can't recall if the check box "authorize without ID" was checked.
I will uninstall ADE and re-install giving attention to the settings before I accept. Once I install I will try to download the e-book.
I hope it works then.