I have a human rigged and animated for my game, I want him to walk around and used a weapon. But not sure how in the logic blocks, to set it up so the run animation plays while he is swinging his sword at the same time.
You can make a own animaton with waking and swinging. Or you can combinate the animations wit the NLA editor.
HG1
You can play two or more actions simultaneous when the do NOT share ANY channels.
Check the Action window for the channels. If necessary remove them with <X>.
Another (but more complex) way is this:
http://blenderartists.org/forum/showthread.php?t=173413