Hi, and welcome! Sorry you ran into this problem - it's been ongoing for a while now, and it is quite frustrating, but there are workarounds that should let you register your books. Here's a summary:
There appears to be a window of time each day when the lookup simply does not work (or at least fails to work for most people); it seems to be roughly 10 AM US Eastern time (2 PM UTC) to 6 PM US Eastern (10 PM UTC). During that window I'm pretty consistently able to use the lookup, with the best success coming when I use Google as the search-database and I search using the title and author (as in "Pickwick Papers by Charles Dickens"). [The other day I was able to register using the Amazon database and an ISBN, fwiw, but the Google/title/author combo seems to work best.]
If the search doesn't work, as you've probably noticed, you see no search results at all. When the search window is open you will usually see SOME results even if the search can't find the specific book you're looking for, but if the search-window is closed there will be no results. In that case I use "skip search" on that and any other books I plan to register at that time.
The trick with the "skip search" pages seems to have to do with the ISBN. I can usually register books by entering title, author, category, and ISBN (with no spaces or hyphens, just the digits), but I've seen many reports from people for whom this method doesn't work. In that case, omit the ISBN entirely. You should be able to register the book without it, and can then use the "edit book details" field to add it if you want to.
I hope that helps you get your books registered, whether you do them by "skip search" or wait for the search-is-working window to open.
Re book-cover images: I like having the cover pics on my books, and the skip-search method does not provide them. Sometimes I'll hunt up cover images online (or just take a photo myself) and upload those, but I've found that if I wait until the search-window is open I can go down my bookshelf list of blank-cover books, click on the "update cover" link, and let the search find the covers - depends on whether I'm impatient for the cover or not!
The problem's well-known, with extensive discussions in the Bugs and other forums; no word on a fix yet, but I hope these workarounds will help.
Thank you very much for your reply. I did find the thread dedicated to this problem, so I posted there as well. You're right, it might just be at certain times of day, because suddenly it's working again, at 5pm Central European Time. I've made the most of it and registered four books!! Thank you again for taking the time. I will try the Skip Search again if necessary, and I'll bear in mind what you said about the ISBN number. Enjoy your day!