Hm, that's strange, and I take it that Close just closes iWeb without changing anything, right?
I can't think of any easy fixes. You could try to "reset" iWeb by closing iWeb and then drag the file com.apple.iWeb.plist in /Users/<youruser>/Library/Preferences to the desktop, and also do the same with any files that you find in /Users/<youruser>/Library/Application Support/iWeb/
Then try to start iWeb again.
If that fixes everything, just move the files you just dragged to the dekstop to the trash. If it doesn't, you can quit iWeb again and drag the files back to where they came from.
Do you have a .Mac subscription? I just tried dragging my com.apple.iWeb.plist file out, and I did not get a question about .Mac when I started iWeb again, but that may be because I have a .Mac subscription set up in System Preferences.
Can you click anything on that screen to go on without .Mac?
You should try to create a new user account and try it from there before you go to more serious steps like reinstalling.
If you already have another user account, try to log in with it and see if it has the same problems. If you don't, create a new user account in Accounts in System Preferences, give the new user admin rights, then log in with it and try iWeb.
OK, we're starting to run out of options. Are you sure that you haven't done anything to iWeb before. It's the same iWeb that came pre-installed in the Applications folder, and you still have it there, right?
Assuming it is, I guess it's time to do a repair permissions, even though it's a long shot. If you haven't done a repair permission before here's the guide.
If iWeb still won't start up, I'd probably do an archive and install of OS X, unless someone else here have suggestions. Here's how. Note the points about doing a back up and also point 11: "You should also select Preserve Users and Network Settings, to preserve network and Home directory settings."