The most common cause of this problem is a corrupt "User Data" directory.
To fix this, open Windows Explorer (not to be confused with Internet Explorer), then navigate to "C:\Users\(your user name)\AppData\Local\Twine" and there should be a "User Data" directory there. Rename the "User Data" directory to anything and then try opening Twine again. If that works, then just delete that renamed directory.
If that doesn't work, we're going to need more details, but usually that does the trick.
Hope that helps! :-)