I am using Windows 98/SE, I.E. 5.5, and had a similar problem with some, not all, secure websites. Solved it by doing the following:
Select TOOLS> Internet Options> Security> Custom Level, then scroll down to near the the bottom to User Authentication> Logon
Make sure that there is a tick mark in "Prompt for User Name & Password".
After I did that, there was no problem with access to any secure websites, including my bank.
I also use Norton System Utilities which includes Internet Security and Firewall.
Also, you might want to be sure that 'Cookies' are enabled, as many secure websites require their use. Again, select:
Tools> Internet Options > Security> Custom Level, scroll down to Cookies> and make sure that there is a tick mark to enable 'per-session' cookies, and if that doesn't work, also tick off to enable 'stored' cookies.
...edited for the addition of the 'cookie' information.
Last edited by LastCall; 27th November 2002 at 01:17.