You have to fight dark aeons if you:

1) Have the PAL or International version of the game
AND
2) Missed Besaid and/or Macalania

You don't need to on the American version, and you don't need to if you only missed Kilika, Djose or Zanarkand.

Speaking of which - go back to Zanarkand and get the treasure there. You almost certianly missed it - most people do.

Anyway, if you got the treasure, the statue should light up. Getting rid of the item will not change anything - opening the chest is what counts. I think even if you can't pick up the item or choose to discard it due to full inventory, it still counts.