Try moving the the launcher folder somewhere else (C:\Legions for example). See if that does anything.
http://forums.legionsoverdrive.com/...of-legions-launcher-bugs-and-their-fixes.614/ 3rd post labeled 3.1 "Launcher.exe doesn't work"
The launcher no longer requires the .NET framework - so that list of fixes is mostly irrelevant. Also - help us to help you, we can't fix when you aren't helping us debug the problem.
It says this when I try to run the file. "Windows cannot access the specified device, path, or file. You may not have the appropriate permission to access the item."
Disable your antivirus protection JUST to install legions and then once installation has finished re-enable the antivirus.
Right-click, run as admin, type in administrator password if needed and enter, else just hit yes. Ignore everything 'Hi!' just said.