I just bought a new pc with windows 8 and have been using the skype app for windows 8 until I needed the features of the desktop version. I got the desktop version and tried signing in and it says "we can't open skype you're already logged in on this computer please sign out and try again. how do i fix this? I am not using a microsoft account on my pc just in case that helps you out.
If you are not using MS-account then you can sign out of Skype Store App by opening it, then going to settings. There is a sign out option for your account (again: if you are not really signed in with MS account).
After signing out you can use the desktop version.
If that wont work you can always uninstall the store app and reinstall it.