Take a close look at a set of certain practices at one of the world's top strategic consulting companies (they've advised most companies from Fortune 50, 100, 500, 1000, and they don't advertise - they don't have to). First of all, they keep a browsable database of "clean" reports from past projects (clean means no company names or sensitive data are enclosed). Second, their consultants can contact any of the other consultants around the world for advise/tip/hint, and those are obliged to respond within 24 hours (if possible).
Keeping an internal knowledge base around is so underrated. Solving an overnight crash (either at 2AM or on a misty day, your thinking performance is not state-of-the-art) gets so much easier when you have some notes with previous solutions saved. Your colleagues might also "have been there and done that."
You may want to argue that do-it-on-your-own attitude is better (for the sake of learning). There are three proven ways of learning: by studying, by doing and by examining how others made it before. So if you really insist, keep that option around when you have some spare time.
Hide your pride. Keeping a strong culture of knowledge exchange goes along with superior quality and performance, bolsters creativity and teamwork. Coming across a tough problem doesn't indicate a hard mining for solution. Go through your team's shared notes/documents, ask around. A key to that closed door may lay around, don't waste your time breaching it.