One thing that I've seen happen on networked computers in my highschool was firewalls interfering with secure connections. You should try first off disabling your firewall (only long enough to see if that's related).. and if that doesn't work, toggle the options in IE (tools - Internet Options - Advanced (scroll down to sectuurity) that says "Use SSL 3.0" or "Use SSL 2.0".. these two are used over secure connections (shopping carts and hotmail, to name a few) and might help out.

I hope that gives you something to go from.