Were you able to sign in at least once or have been using it regularly? Or has it never come up?
If the former, as a first thought, you might try renaming the client and contact cache for Messenger to see if that’s causing grief. You can get to by opening up the Run box (WinR or right-clicking the Start button and choosing Run), inputting %localappdata%\Microsoft and rename the Messenger folder, and as well as the Windows Live\Contacts folder.
If it’s the latter option (or you can try regardless), another thing you could attempt is see what happens when there’s no network connection and/or you disable all your imaging devices (webcams, virtual webcams, scanners). In some cases (admittedly most (hopefully all?) of these problems were fixed by the 2009 version), when Messenger initializes /enumerates these devices on startup, it can get stuck.
To try, open up Device Manager (run devmgmt.msc or right-click on the Start button and choose Device Manager), right-click each of these types of devices, then choose Disable device. Then kill the msnmsgr.exe process in Task Manager and try running Messenger again. When done, right-click the disabled devices and choose Enable device.
Lastly, a visit to the Event Viewer → Application log is always a good idea to see if anything gets logged when Messenger starts. You can get to the Event Viewer by running eventvwr.msc or right-clicking the Start button and choosing Event Viewer. When the viewer opens (which is always slow), choose the Application log and review any warnings and errors that happen when Messenger starts.