I don't know if action is a no no, but take a look at Ico, Clock Tower 3, Fatal Frame 1/2, Eternal Darkness(GC only), Silent Hill 2/3/4, or the Resident Evil games. Also, there's a new game called Obscure, although I don't know if it's going to be on GC or PS2. It's already out on PC and is $20. Decent action adventure in the tradition of Resident Evil.
There are other games like this, but those and all those I listed might fall outside of what you're looking for.
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