You should contact Windows Live Support. Nobody here, or on other unofficial forums for that matter, would be able to help you with such issues.
So contact Windows Live Support with as much details as possible (more than the one you gave in your post. eg: OS, Messenger version, do you have 3rd party addons for Messenger, etc):
http://support.live.com/eform.aspx?productKey=wlm...&ct=eformts&scrx=1
Follow the next steps in case you end up in the help pages/faq (http://help.live.com) after using the above support link:
- Pick your Windows Live Messenger version (this would be WLM 2009 I assume).
- Click on one of the topics in the left pane (doesn't matter which one).
- Click on the "Get more help" link in the lower-right corner.
- Click on the "Get support" link in the main window.
- Fill everything in with as much details as possible in the form.
Also note that what you call 'MSN Groups' are not what they are called! 'Groups' are now something completely different. So make sure you use a proper naming: 'group _chat_', and make it even explicitly clear that it is not the new 'groups' feature you're having problems with.