when I try to install Worms Armageddon, my computer says its dxmfc.dll file was not found? How can I fix this?

first reinstall the game, then go to http://wa.team17.com and download the 3.6.28.0 beta update and apply it, when it asks to install the "patch" click yes.

now run the game.

Wait, does this error come up when you're installing the game, or when you're trying to run the game?
If it's a problem running the game, then do what Franpa said and it'll work. (it's a thing with old versions of Armageddon.
If it's a problem while trying to actually install the thing, well it's not the first time that's been reported (http://forum.team17.co.uk/showthread.php?p=473437#post473437).