Steam Offline is such a hassle, whenever you need it to work, it somehow manages to break...I'm assuming you have 'Don't save account credentials' unchecked and still getting this error?
If so, I second pups suggestion of just reinstalling Steam itself. Just backup your 'steamapps' folder and bring it back once Steam has successfully reinstalled and verify your cache. That should reduce the need for downloading everything again; had to do this personally myself a few times and it's not too painful.