First of all, please accept my prayers for your father and your family in a very difficult time.
You may want to try repairing .Net Framework to resolve the problem with OneCare not being able to open. It may also be the cause of the problem with the Network and Sharing Center.
To repair .Net Framework 2.0 on XP:
Open Control Panel
Select Add or Remove Programs
Locate Microsoft .Net Framework 2.0
Select the entry and when the installer launches, select Repair.
Reboot when it completes.
Alternatively, see this KB article:
http://support.microsoft.com/kb/306160
To remove a corrupt .Net Framework install, use this tool:
http://astebner.sts.winisp.net/Tools/dotnetfx_cleanup_tool.zip
The download of .Net Framework 2.0 can be found here:
http://www.microsoft.com/downloads/details.aspx?familyid=0856eacb-4362-4b0d-8edd-aab15c5e04f5&displaylang=en
To repair .Net Framework 2.0 and 3.0 on Vista, see this blog entry:
http://blogs.msdn.com/astebner/archive/2007/03/26/how-to-repair-the-net-framework-2-0-and-3-0-on-windows-vista.aspx
If the above does not resolve the problem with OneCare, please contact support - the FAQ explains how to do this from a PC that does not have OneCare installed, but it does require you to know the LiveID for your OneCare subscription to reach your support options beyond email.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
Unofficial path - send me an email at sboots@mvps.org with a subject line including "OneCare" (to get past my spam filtering) and in the message body, tell me what country you are in, your forum nickname, and paste a link to the post to which you are replying. I am not online 24x7, so you may be waiting for a reply, but I'll do my best to hook you up with support.
-steve