I got hit with the error "Can't open Skype. You are already signed in on this computer. Please signed out try again." upon trying to sign into Skype. I figured out how to fix the problem so now, I am sharing how I got around to fixing the problem. Please note that this may be a broad error message so there may be other issues that also throws out this error. Basically, this fix may not be a fix all for everybody but hopefully, it will fix yours :-)