If you fail the quest "Before the Storm" in Skyrim, can you not do any quests after it?

No, you have to take the quest. You can also pick up a quest on the outskirts of Whiterun that will start you on another questline with the Companions.
Answered by kgb agent Vernaliza P on Tuesday, March 27 2012 at 11:58AM EDT
Source: kgb.com