It is just outside the inner castle wall, by the kitchen. The kitchen is in the north-eastern portion of the castle.
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Assuming that you used the bucket of water with the drain, the key should be here in the mud http://img502.imageshack.us/img502/6241/varrocksewers.jpg
The key is stuck down a drain behind the kitchen in the castle. Go get a bucket or jug and fill it with water at any water source and the sink in the kitchen gives you water (if you did not bring a bucket, up the stairs there is a rooms at the corner and you can get a bucket in there). Use the bucket of water on the drain and the key will be washed into the sewers. Enter the Varrock sewers using the manhole located immediately east of the castle's keep. Follow the north-western path until you get to a stream and go to the small corner. Search for a rusty key on the ground; it will not appear on the minimap. Grab it.
bucket of water
tiki torch and hook the drain and tap the drain to get spa key card3
just head down, into the sewer, now just follow the hallway north. Go to your left, and you will see a little glint where the key is, if you already don't see it.