The latest Windows Live Messenger won't alter your ability to browse websites at all.
Make sure that you download Messenger Plus! Live from
here.
Also, check your Add/Remove Programs (Programs & Features on Vista/7) for any of the programs in the following thread:
Messenger Plus! Live Disappears after restart
Although you may not be aware of installing any of them, you should check just incase as some of those programs could have become installed without your knowledge