I have the same problem but it is only with one database. The rest work. I cannot find any help on this anywhere. I was using the trial and most likely will not buy because of the poor support. This was the main feature I was going to buy for.
What settings do you see when you open the file and bring up File | Sharing | Instant Web Publishing?
I know the original post is dated ... but I just struggled with the No Databases Available, too. In my case, the file I was trying to IWP was hosted on a server. You can't IWP a file on FileMaker Pro that resides on a server. Duh... that was obvious in retrospect.
I found this out by creating a new local database with one table and field. It showed up on the File -> Sharing -> IWP window.