first thing to check would be if you actually own the expansions you think you own (the free expansions for owners of expansions on Making Fun expired). Go into the "Account" tab and look at the boxes presented to the left. If they are colored, you own them. If they are grey, you don't own them. If you are right about what you own, everything should be colored, except for the Nocturne box.
Assuming that checks out, let's try to start a game without respecting familiar cards. Go to "New Table", then click "Create Table". You should be listed as host on the right side of the screen. Click "Advanced options" (the right-most button of the three below) and make sure that the checkbox for "Respect familiar cards" is unchecked. Go back by clicking "Basic Options".
Now the fast thing to do would be as josh suggested and just start a game against Lord Rattington by clicking "Add bot", then "Ready". If you want to play against your son, you can alternatively wait until he joins the game. Now you should have a Kingdom that is randomly selected from all cards you own, so should not consist of Base cards only.
If you actually own all cards (besides Nocturne) and still only get base cards in a game on a table that I described above, please post again, so we do more tests.