Really sounds to me like the Net Nanny may be the culprit, though I am not actually certain since I am not familiar with the program.
Have you checked the Restricted Sites on your Internet Explorer, your firewall and also the Net Nanny to be sure that these are not being blocked by these programs?
I see you are logged on as administrator, are there other user accounts on the computer and if so, can you log onto the computer with one of the other user names and access these pages?

Your router software may be blocking access. To find out if your router is causing the problem, unplug the network cable that runs from your cable modem to the router, and plug it directly into the network (ethernet) jack on your computer -- temporarily cutting the router out of the loop. If that solves the problem, check your router's manual to see if it can block or unblock certain ports. It's unlikely, but it may be configured to block port 443, which is used to make secure connections.

Your java is out of date is one thing I notice, though doubt that would cause this. But you should go to
http://www.java.com/en/download/manual.jsp and download the offline installation for the java and save it to your desktop.
Then go to Add/Remove and uninstall all java programs listed there.
Once you have done that then install the new download.
Then go to this link to verify installation;
http://www.java.com/en/download/installed.jsp