The same thing happened to me. I couldn't add any books and calibre wouldn't look at the device. Syncing didn't help and anything I added to my sd card simply didn't show up on my reader.
This is what I did to restore my Kobo after going through this forum and looking for suggestion.
1) Initially I didn't care about the free books
I connected my kobo to my computer. Opened the device via my computer, went into the ".kobo" folder. Renamed the "koboreader.sqlite" file (I called mine koboreader.sqlite.old) and then ejected the kobo.
The kobo then restarted and created a new database which was empty of books. I resynced via the desktop application and returned the books I bought to the kobo (none of the initial free books were there of course). I could add new books and it recognized the books on my sd card.
2) Then I decided I wanted the free books back.
I found this thread and everything worked like a charm to restore my kobo to the day I first turned it on.
https://www.mobileread.com/forums/showthread.php?t=94789
If I was to do it again I would just restore it to the original database (the link above).
That was a couple of weeks ago and I have adderd, subtracted and used my kobo about 4 hrs a day since then. Everything still works fine.