I'd like to give you more ideas or advice, but boyo I'm stumped. The only other thing I can think of is whether you've inadvertantly shut off getting automatic game updates from steam, and the mods you are trying to enable are all dependant on the latest version of the game.
When I get to the main menu where I can select to go into the MODS menu, my version of the game says it is "1.0.3.144" at the bottom of the desktop screen.
If yours is showing an earlier version number than that it might be the cause of your trouble. If so, make sure you haven't accidently told steam not to automatically send you updates to the game. The other thing to do would be to verify the integrity of your game 'cache' through stream. What that actually does is looks at your game files and makes sure they aren't outdated or altered in some way. If in the past you've used one of those mods that tell you to 'replace the original game file' with 'this version of the game file from the mod', the verify integrity of the game cache will restore the original Firaxis-made version of any such files. Copy any such altered files somewhere safe in "My Documents/" before you do a verify integrity of game cache.
If you don't know how to do the verify thingie, and want to try it, drop a note back here and I'll outline the steps needed. (I think I may already have a set of instructions up on Mediafire somewhere, but I can't remember for sure).