Reset your computer. Then try to log in to skype again. It's normally because skype thinks you are already logged in and has closed. Because of this when it relaunches it asks you to sign in, but because you are already supposidly signed in tells you that you can't sign in. Once you turn your computer off it signs you out all together so when you relaunch skype you should be able to log in.
This normally works for me (and happens quite frequently). If this doesn't work, sorry I don't know