IPhone – How to play all songs I own by an artist in itunes

As of iTunes 10 (or possibly 9), the main library window has the option to do exactly what you want. You need to have it in Album List mode (View menu -> as Album list; or the 2nd option in the view controller:

Then select the "Album by ..." pulldown and select Album by Artist/Year:

You should be all set and have a nice organized list of albums sorted by artist and year.

When iTunes shuffles through a playlist, library, or other list, it only will shuffle among items for which the "checkbox" column is checked. By default, this would include all the items in your library; only if you uncheck the box for a song would that remove it from the list of songs to shuffle.

It sounds as though your library is set up with all the songs unchecked. If no songs are checked to be included in shuffle, one gets the behavior you describe. The solution is to go to your library and make sure all your items are checked, not unchecked.