It's now clear the problem may be Firefox or IE8 or one of the security/anti-malware apps you are running.
You can download and install Opera, being sure to leave the default settings. This may well allow you access to the Applebank site when you need to access it. Feel free to surf other sites using IE8 or Firefox.http://www.opera.com/
A more cautionary approach:
Since you've already used Ubuntu 9.10 successfully, you could choose to continue using it for banking and browsing other secure sites which require a secure connection. It is clear to me you have done your homework and protect your Windows machine as much as is possible. Your efforts and diligence are to be commended.
Please let me know what you think and we'll proceed from there.