It sounds like there is some confusion as to what should happen with internet shortcut links.
Have you tried making IE the default browser and then re-make Firefox the default one?
To make IE(6) default:
Click Tools and then Internet Options.
Select Programs
check Internet Explorer should check to see whether it is the default browser.
click OK
Close and restart IE with Firefox closed!
Check you shortcut.
Close IE and start Firefox.
Make Firefox Default:
Click Tools and then Options
Select Main and make sure the bottom check box is checked and click the check now button too.
I tested it here and it does work but dont rely on any shortcuts from changing automatically.