Have a "smart" FAQ. Make the primary section be the most frequently "asked" questions, based on analytics. Show only the top 10, with an options o view more. Have an obvious link to view all and an obvious text field to search all. Have a section at the bottom of the detailed answer page that asks "did this answer your question?" and an option to add an explicit question to the FAQ if it does not. If they enter an explicit question, try to search one more time against this text. If no results are retrieved then ask them if they want to be contacted if the answer to this question is ever added to the FAQ, and if so enter an e-mail address.
This design does several things: it "crowdsources" the most popular questions into a top 10. It allows for quick search and/or browsing activity. Finally, it engages the user by asking them to add their own question and allows you to capture an e-mail address that you can use to potentially respond at a later date.