In order to slay the dragon, you need to open up the dungeon using the keys, and solve the various puzzle rooms for tokens of your success. You also need to solve two metapuzzles: one using the pedestal puzzle answers, which opens the golden door, and another using the statue puzzle answers, which gets you a weapon from the Mystic Circle. Approach the dragon with at least seven quest tokens, and your weapon, in hand, and you will defeat it. (If you get all eight quest items, you get a special bonus in the runaround.)

After defeating the dragon, teams embarked on the runaround to save Cody Pumbleton.

Strange Bedroom

The answer that goes with the Strange Bedroom is CAESAR. When you speak to the girl, she says three words. Each of the words she gives you can be Caesar shifted into a word that fits the question the girl asks:

Where you play:             RIVER -> ARENA
What makes you feel better: BUNNY -> SLEEP
Something made of gold:     CHAIN -> INGOT

Give these responses and the girl gives you a crystal amulet.

Shadowy Maze

The answer that goes with the Shadowy Maze is SENSED. Treat each letter as a direction to follow to turn the lights on in the maze. When you do, you find the crystal armor.

Dark Room / Minstrel's Hideout

The answer that goes with the Dark Room is MARCO. Go into the room and say "Marco"; a voice will respond "Polo". Do this enough times and you'll catch the minstrel, who will tell you a tale and then give you the crystal shield.

Knight's Watchpost

The answer that goes with the Knight's Watchpost is ANAGRAM. The knight asks you to find the true nature of his helm of "insentient fright". Plug that into an anagram generator (or sweat really hard) to find that the only sensible anagram is "infinite strength"; say that phrase in the presence of the knight, and the crystal helm of infinite strength is yours.

Dojo

The answer that goes with the Dojo is ROCHAMBEAU. Attempt to defeat Dark Falcon at a game of rock-paper-scissors (either using "attack Falcon with rock" or "throw rock") and you discover that he only knows how to throw rock. Hence, throwing paper will defeat him, and induce him to give you a crystal badge.

Barren Room

The answer that goes with the Barren Room is RUSSIAN CHESS. When you attempt to answer the Sphinx's riddle ("what's black and white and red all over?") with the standard answer ("newspaper"), she complains that the riddle asks for something red, not something read. Russians are red-- and chess is played with black and white pieces. Say the answer to the Sphinx and she will allow you to take the crystal vial of healing potion.

Music Hall

The answer that goes with the Music Hall is MACDONALD. Play the opening notes of "Old MacDonald Had a Farm" on the xylophone to get the crystal boots.

Kitchen and Perilous Tunnel

The answer that goes with the Kitchen and the Perilous Tunnel is AIRPLANE FOOD. Ask the gourmet chef for airplane food and she will give you a silver tray with garlic bread, salad, salmon, and cheese. Each of these five items either distracts or repels one of the monsters in the Perilous Tunnel; if you drop the proper item in front of each monster, it will be subdued and allow you to pass. At the end of the Perilous Tunnel is a set of crystal gauntlets.

Golden Door (Key Metapuzzle)

Exactly one letter of each key answer can be removed to yield a new word. Furthermore, notice that the key answers are each of unique length, giving you an ordering:

       AFT = F + AT
      FREE = R + FEE
     CHAIN = A + CHIN
    PLACID = C + PLAID
   NEUTRON = T + NEURON
  MISUSING = U + MISSING
 RETRAINED = R + RETAINED
FEATHERING = E + FATHERING

Write FRACTURE on the golden door to clear the path to the dragon.

Mystic Circle (Statue Metapuzzle)

If you map out the dungeon, you find that it looks suspiciously like a crossword grid. In fact, the eight statue puzzle answers can be filled into a map of the dungeon:

Meanwhile, you should have noticed the Roman numerals painted throughout the maze. Read the letters at each numeral in turn to find the phrase ICE LANCE. Say this in the Circle Room to receive the lance.

For a fully annotated map of the dungeon, see here: map.pdf