Hi Capetonian
I suspect the problem is that you are using IE6 which was released in 2001! Without going into a long history, the latest version supported in Windows XP is IE8. As you are using Windows 7, you should use at least IE9, which was supported from Vista on, and included support for HTML5 and other features which are used by most sites and especially banking (which you mention). At some point these sites will or have withdrawn support for IE8 or earlier.
In order to ensure that you are protected as much as possible by the latest security fixes, I suggest that you download the latest version which is IE11 and then ensure that you install all the updates to take advantage of the important security fixes. You should then find that all the sites you mention work properly. It is available from microsoft.com; click on "Software & apps" and then "Other software & services" followed by "Internet explorer". My advice is not to be tempted to download it from anywhere else.
Alternatively try another browser!