(Mr Mixture, etc)...
You rang ?
I would start with the simple side and concur with CATIII-NDB that you should try either a newer version of Internet Exploder, otherwise download the latest version of Firefox and try that.
The second question is ... does this only occur with "secure" websites (finance, ecommerce, email etc.), or is this fast becoming par for the course during your "normal" internet browsing (e.g. news websites, PPRune etc.) ?
Are you able to access the sites themselves and just not sections of them (e.g. able to see homepage, but not login), or are you not able to browse to your bank's website full-stop ?