The Ruin Key (いせきのカギ, Iseki no kagi?, lit. Key to the Ruins), described in-game as "A key found in the ruins under Madra", is a Quest item in Golden Sun: The Lost Age, both found and made use of in Madra Catacombs underneath the town of Madra. First off, it can only be found on a later visit to Madra, when Piers has joined your party, because you require the Frost Psynergy to freeze a necessary puddle into an ice pillar in the "outside area" of the catacombs underground.
Upon entering the upper left of the three visible doorways into the northwest structure, you are led to a room where a chest is sitting on top of a bookcase out of reach. Use the Tremor Psynergy (bestowed by the Tremor Bit, also found in the Catacombs) in the direction of the bookcase to the right to shake the chest off into the abyss. Go back "outside" and enter the structure through its bottom door, and head straight up into a room where the chest from earlier is now on your left. It contains the Ruin Key. Head down into the hallway and enter the doorway to the right, and climb down the stairs to a big, red-colored door; use the Ruin Key here and it is used up as the door opens and you can collect your overall reward - the Moloch summon sequence.
The Ruin Key can be sold before making use of it for 172 Coins. Since it counts as an Artifact, it can be bought back at any point later from any item vendor for 230 Coins.