Early in the game I found the puzzle box and continued exploring, picking a couple of locks as I moved deeper into the ruins. I made it to an area called Deep Ore Passage or something like it, then returned the puzzle box to Hasphat, who told me to return later and he'd give me a key. I continued adventuring and forgot all about him until much later.
I eventually returned for the key and went back to the ruins, but I can't find any areas that I hadn't already been to. What door does his key unlock?

Haven't gotten around to doing this quest yeat but from what i hear all the key does is unlock all the locked doors you came across instead of having to use lockpicks or a unlock spell. If you have been everywhere in the ruins don't worry about it you probably unlocked all the doors without the key.

There's a lock door there in the ruin. but most probably you already pick it because it's the first locked door you'll encounter. which mean that key is particulary useless.