It sounds as if the intro movie is still running thou it shouldn't when you are in the Game Menu has been launched. Also you should be given a warning if you try to launch a second Crysis.exe!
Have you tried launching the game from the MWLL_Launcher.exe found in Crysis/Mods/mwll? This should give you a Menu where you can select either "Launch 32-bit Game" or "Launch 64-bit Game", after executing that an intro movie is displayed, press "Space" to skip the movie and you will be met by the Game Menu where you have to select Multiplayer, and any server with a low ping for optimal game experience.
You can also launch the game via Crysis own shortcut with the added code -mods mwll after the quoted text in the Destination link, e.g. "...\Crysis\Bin32\crysis.exe" -mod mwll
Don't run the standard Crysis and then run the Mod via the built in menu, that will start you in Singleplayer, as well as run its own actionmaps afaik.
If the above does not work, you might want to re-install it?