Do you know exactly what AdobeID was used when you first purchased these books?
Was the computer authorized with a specific Adobe ID, or did you leave ADE (Digital Editions) to 'run without authorization'?
If you were running without explicit authorization when you first downloaded the books,
it may not be possible to get out of the hole unless Kobo can allow you to download effectively new copies.
Do you have any of the .epub files for those purchased books?
If so, you can check how it is authorized.
You may be able to do that with ADE and asking for information on the book (ctrl-I).
It may refuse to give the information, in which case the orignal ID can be extracted but it is a little awkward.
I will fill in detail if you find you might need it.