This is one of the less-charming known issues with ADE. If you don't have/register/enter an Adobe ID account when you register ADE, then your books end up being tied to that particular computer and non-transferrable unless stripped. You also can't redownload them if anything happens to that particular install.
I hope you had good un-DRMed backups of your paid purchases, or could possibly restore your old ADE install from a backup of your system so that you can make a backup much like this
other Kobo user had to do.
ETA: This particular error message tends to happen because the Adobe content servers think the license has already been fulfilled (i.e. downloaded) by another, different user/install of ADE. Sometimes it does so wrongly, especially with library books.