Happened to me, and I found the way around it. Here's how to fix the annoying problem:
Go to My Computer and click on the Hard Drive. Navigate your way to C:/Program Files/Microsoft Live and find the folder called "Messenger". Right Click on it and delete it.
Next up, click on the following link:
This will attempt to download an install cleaner. Save it and open it. Once it's running, use the instructions to find and remove all traces of Windows Live Messenger.
Next up, download this:
It's the Windows Live installer. Run it and re-install Windows Live Messenger. It'll now work again completely fine.