There are 5 possible dungeons that the fang can be found in. The location differs from one
game to the next. The only one of the five dungeons that has a known bug similar to what
you are experiencing is volskygge. The gate remains closed and the handles are locked in
place. If this is the same dungeon in your game that bugged on you you can still get
access to the word wall by scaling the mountain side. Simply keep pressing the jump button
to make your way up there, it can be a pain though. Unfortunately, there is no mention on
how to retrieve the fang. If it is in a chest next to the word wall then you can still get
it, if it's inside the bugged door then there is no known way, as of right now, to work
around this bug.

You can, of course, load a previous save before getting the quest and hope to get a
different location for the fang. In case you didn't know bethesda's games are buggy as
hell so it's always recommended to make several save files in case something like this
happens.