Mods that where not updated for 3.13 and that contain an altered .dll or some specific xml mods will crash on 3.13 no matter what you do. You might want to make sure that they where updated for 3.13.
also the two mods directories are:
...\documents and settings\<username>\my documents\My Games\Beyond the Sword\MODS
and
...\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond The Sword\Mods
(as posted by T.A. Jones)
if you put anything into the first one of those - it will crash, this directory should not even be there it serves no purpose other than to crash people's game
Edit: a simple test whether it is a specific mod or your install:
create the following directory:
...\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond The Sword\Mods\TestMod
and leave it empty. Now start the game and load the mod called "TestMod" if it crashes it is your install, if it loads and shows "TestMod" in the upper righthand corner of the start menu its probably caused by the mods you try to load...