Its not possible for Minion to get past the splash screen (Just the Minion logo) with out a .minion folder or minion.xml for that matter. If it can't make that file or read it Minion fails right away and you won't even get to a loading addons screen. So I'm guessing maybe that your windows user folder is set to a non default location and the .minion folder is located there.
It looks like the default user folder path is stored in the system registry and can be
modified (I dont suggest it, just showing you it can be done), if its not something you modified maybe its something your system manufacture maybe changed so that your windows profile would be on a separate partition or disk with more space?
Do you have other hard drives / partitions on your system? Can you look around for a .minion folder on them?
Maybe an easy way to find this. When you download a program in Chrome or whatever browser you use where does it save the file? Default path would be C:\Users\<your username>\Downloads. Is yours different? If so try looking in the folder before that for the .minion folder.