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Didn't you find the dog's corpse? It will allow you to complete the quest - unfortunately not with the optimal result. To save the dog, you have to reach the bottom level within four in-game days...

Well, you need arrows. If you have some, "e"quip the bow in the missile weapon slot, equip a stack of arrows in the missiles slot, and use "t" to Target the troll.

Ranged weapons will hurt trolls...