My character is level 14, and I have slept countless hours to try to make it work, but the Dark Brotherhood never send assassins in my game. I have the GOTY version of Morrowind, everything is installed, and Tribunal is selected in the data files. I know for a fact that it's working because I am using quite a few mods that require tribunal, on top of the fact that Wrye mash says it is running. Is it possible that I could be running a mod that messes up the script that allows the DB to attack?

Could be, but we won't know unless you post your Load Order.

Also, if you talked to Apelles Matius in Ebonheart about the situation (but now forgot you did) then no more will come attack you.