Short and sweet: I've finished the quest doing everything Dagon's way, but when it comes time for me to touch the alter for the last time, the dagger disappears and nothing happens. I've waited, fast traveled away and back, ran away and back, danced, and sacrificed like twelve goats.

Anyone had the same problem or know how to fix it? Also, I don't have the latest patch, so it may have already been fixed. No internet for the Xbox.

Mehrune's Razor issues have been previously patched.
See this thread for a list of all fixes...so far. http://www.gamesas.com/topic/1255755-game-updates/

To fix your particular issue:
1. Load a previous Save and try again
-OR-
2. Find a connection and update to Version 1.6.90.0.6, which was released for Xbox 360 on 06/08/2012.

Hope that help