Just like a hat, you must equip a deck to use it! And you need to make sure you put cards in that deck!
Press B on your keyboard when you're not in a duel. This will open your Backpack. Select the Tab at the top for your backpack that shows your Decks. One of the decks in your backpack MUST be equipped for your cards to be available in battle. Select the deck you want to use and press the closed hand icon at the bottom of that panel to equip the deck.
Next, Press P to open the deck itself. Your available cards will show on the right, and the deck will show on the left. Click the cards on the right to move them into your deck. Build your deck from all your cards, and THEN go into a battle.
If you still only see the spells from your wand, repeat the above instructions.
If you want the prize, you have to build the ladder rung by rung. There are no shortcuts.