Hi Servalan,
Problems accessing secure sites are almost always caused by one of 3 things, usually following an automatic update.
1. Browser misconfiguration - Download a copy of either Opera or Firefox, if the problem persists you know this isn't the problem.
2. Firewall Configuration - Uninstall any Firewall software, such as Zonealarm, or Internet security applications, such as Kaspersky Anti-Hacker or Norton Internet Security - reboot your machine, does the problem persist? Windows firewall shouldn't cause this but disable it just in case.
3. Malware infestation - Run a full AV sweep of your machine, then run both Adaware and Spybot s&d scans of your machine. As a last resort locate the hosts file (c:\windows\system32\drivers\etc if memory serves) and rename it to hosts.bak - reboot.
Please remember to re-install any security software after testing
Hope this helps
Rgds
Havelock