I just got Morrowind on Steam and if I try to play it, the game will load but it will freeze at the main menu screen without any text, just a background. The error message that comes up is: "Music Error: Can not play file. Data Files/Music/Special/morrowindtitle.mp3". I already tried uninstalling and reinstalling the game as well as verifying the game cache, but none of that worked.

This is usually from a corrupt install, but there are other things that cause this too.

Make sure Windows Media Player is the default program for playing mp3 files, not something like iTunes.

You're probably on Vista or Windows 7, right? It is best to install outside of Program Files. (this avoids many problems that can occur with programs in Program Files)
You can just drag/drop your game somewhere else, like C:

One other thing to try if you still get the error, is to install the game with nothing running in the background, including your anti-virus.

How do I change the install location of game files on Steam?

Mmm, I'm running the Steam version of Morrowind under Windows 8 and the default program for reading mp3 files is not Windows Media player; the game just works fine, so I suppose that's not the problem.

On the other hand, Steam is installed on a separate wolume of my hard drive. Maybe, it's a reason.

Did you try running the game as admin? Before completely reinstalling your Steam folder...

I tried running that game as admin, but that didn't work either.