I just took a look -- at
http://home.myhughesnet.com/ -- your log in should be your HughesNet e-mail address and password. Got those saved in Firefox? Have you looked to see if they're correct (edit-preferences-security-saved passwords)? All that gets you in to the web page.
The other log in, when you go to "My Account," is (usually) different; e.g., not your e-mail address, not the same password (maybe). Got that stashed in saved passwords?
I'm running Firefox 6.0.2, HughesNet, and no problems.
Hope this helps some.