If you keep experiencing crashes when starting ths game...
This is for you. If reinstalling doesn't help, what you need to do is to go into the game folder located at Drive:\Whereever steam is\SteamApps\common\Half Minute Hero and then deleting the video file in the res folder. The game apparently cannot play the file thus it will crash every time it tries to play the video.
EDIT: For those still having problems after deleting the video from the directory, try setting the launch options to "-windowed". This helpful tip is provided by Daniel.
Second EDIT: If those two are done and yet your game still crashes, try disabling the "enable steam access in-game" option. This helpful tip provided by MeePwn.
Third EDIT: If you still have problems, try forcing the game to run in 640x480 resolution. This tip is provided by Queen's ChunKiu.