Messenger should be listed in Programs and Features. Select to uninstall Windows Live Essentials. Then select uninstall and you will be presented with a list of Essentials to uninstall. Select Messenger and uninstall. Make sure Messenger is not running when you uninstall it.
Reboot and try installing Windows Live Messenger again.
If that doesn't work uninstall it again. After the uninstall you may have to manually delete any left over Messenger folder and files. I believe they are located here,
Windows 7------C:\Program Files (x86)\Windows Live
Windows Vista-C:\Program Files\Windows Live
Only delete the Messenger folder not any others.