What error are you getting when trying to reinstall?
Run the Cleanup tool - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=828910&SiteID=2 before trying to reinstall OneCare.
However, OneCare is not the reason for some web sites not being able to be found or load. If the web browser can get to the Internet, OneCare is allowing it access. OneCare does not filter any web sites.
If Windows Security Center is reporting that you have no protection installed, that would be normal if you have removed OneCare. If, however, you are getting popups about security problem, advising you to download and install a "product" to scan your computer, your PC is infected and that infection will need to be dealt with before you can install OneCare or most other security products. That may also be the reason for some web sites being unavailable.
You can contact OneCare support (via email as a trial user) for help.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
If you are in North America, you can call 866-727-2338 for help with virus and spyware infections. See http://www.microsoft.com/protect/support/default.mspx for details. For international information, see your local subsidiary Support site.
-steve
