I'm using Skype version 4.2.0.169. I find it really irritating when after signing out once, it doesn't sign in, saying "Skype cannot sign you in because you are already signed in on this computer." The only thing that seems to fix this is to reboot the computer. But I found an easy workaround.
Open Task Manager and go to the processes tab.
Here, search for the 'Skype.exe' and 'skypePM.exe' processes. Now, select each of them, and click End Process. Skype will be completely closed now.
You could also exit Skype normally, but the second process would be running.
Now, start Skype normally and sign back in. It should be working normally now. I tried to find this solution online, but couldn't find it anywhere. Good luck. If it doesn't work, rebooting will certainly work.