If you want a one-button solution for this, go to Playlists in the sidebar, right-click it and create a new Smartlist.
Set up the rules to include all your music, including or excluding certain categories if you want. (e.g. "Media Sub Type is not Podcast", "Genre is not Classical")
Under modify results, select "Shuffle" from the drop-down list.
Now open up the Car Radio playlist group, and delete one of them.
Rename your new Smartlist to ##. Shuffle All where ## is the number of the Car Radio button you want to replace.
Drag your Smartlist into the Car Radio group.
Now you should have a button across the top of all "Playing Now" views which you can press to shuffle all tracks in your library.
At the bottom of my post, there's a link describing how you can create a Smartlist to play a random album (rather than random tracks) which might also interest you.
You can use the same process described above to make it (or any other playlist/smartlist) a Car Radio button.