Browser problem with https pages - Help!

I am using IE 6.02.0026 on ME and have the following problem:
Can't get to pages that have something to do with https(SSL perhaps?), and in some cases ASP - but I think in those cases they are trying to run a script with https page referenced.

It seems to be random, but here is one page that is consistent:
URL
I get this right after I try to login. It happens on other requests as well, like the signon.cfm page for my bank account.

Driving me nuts. I live in Nepal so there is very little support, and I am wondering if my laptop got a virus somehow or some security-related file is corrupt. I checked the dates on all the certs, and they are ok...but after following the instructions on the page that always get returned in these instances, I don't have a clue.

I am hoping a techie here can help me figure this out, you are my last chance.

Thanks,
Jig



Server not found:
The page cannot be displayed
The page you are looking for is currently unavailable. The Web site might be experiencing technical difficulties, or you may need to adjust your browser settings.

--------------------------------------------------------------------------------

Please try the following:

Click the Refresh button, or try again later.

If you typed the page address in the Address bar, make sure that it is spelled correctly.

To check your connection settings, click the Tools menu, and then click Internet Options. On the Connections tab, click Settings. The settings should match those provided by your local area network (LAN) administrator or Internet service provider (ISP).
If your Network Administrator has enabled it, Microsoft Windows can examine your network and automatically discover network connection settings.
If you would like Windows to try and discover them,
click Detect Network Settings
Some sites require 128-bit connection security. Click the Help menu and then click About Internet Explorer to determine what strength security you have installed.
If you are trying to reach a secure site, make sure your Security settings can support it. Click the Tools menu, and then click Internet Options. On the Advanced tab, scroll to the Security section and check settings for SSL 2.0, SSL 3.0, TLS 1.0, PCT 1.0.
Click the Back button to try another link.



Cannot find server or DNS Error
Internet Explorer

I've reinstalled IE...no, wait, I had the problem in IE 5.5 and loaded 6 hoping that would fix things. It did not. Thanks...I am desperate as this is the only way I can check my bank account.