This quest has (at the time of this writing) what seems to be a design bug. It's possible to get the journal without first obtaining the key (by picking the lock). However, getting the journal infects you with a poison (Touch of Zanzil) that makes you unable to use stealth, and picking the zombie's pocket is the only way to get the key (it will not drop if you kill it). Since the pickpocket skill requires stealth, and since the only way to move on to the next stage of this quest chain (curing the poison) is to return to your trainer with the key, if you get the journal before the key you will essentially become stuck. You will need to use an anti-venom spell, potion or item to get rid of the Touch of Zanzil, and then pick the zombie's pocket.
Though this quest was reported broken as of patch 3.3, it now appears to be working properly under patch 3.3.3. The Duskwood Chest will properly drop Klaven Mortwake's Journal and allow you to complete the quest chain.
I noticed that this quest was reported as broken after patch 3.3. I'm running 3.3.3 (as of 21 Apr 2010) and was able to successfully loot Klaven Mortwake's Journal from the chest at the top of the tower. —The preceding unsigned comment was added by Robdango (talk • contr).