Firefile.php will not open in browser at all

[WisdomSeeker]

I just installed the Firefile Firefox addon, and now I'm trying to set it up so I can use it. But I cannot link Firefile to my Firebug, because I cannot even connect to the firefile.php on the web.
Our website is a fresh WordPress installation, latest version 3.5.1.
I set the permissions of the firefile folder and of the firefile.php file to 777.
But when I go to MyDomain.com/firefile/firefile.php
...I get a 404 error.

What am I doing wrong?
I tried it in Firefox and in Chrome, both latest versions of the browser.
Thanks a lot for your help!

[WisdomSeeker]

After trying to everything I could think of to fix this, I called HostGator support and they said I was getting the 404 error because I had set the permission wrongly - 777 is was good apparently... They needed to be 755 for the FireFile folder AND for the FireFile.php file. No other combination of permissions works.
But now I have another problem: when I go to my MyDomain.com/firefile/firefile.php, and after I login with the username & password that's inside my firefile.config.php, there's a message on that same page that says:
"Firebug Status: Active
FireFile is now active and will ask you to register this site."
... but FireFile is not asking me to register this site at all... There's no such message anywhere, not even in Firebug. And I cannot even create an account at http://www.firefile.at/register, since there's this message there:
"The BETA program is currently closed. Please try again soon."
Maybe that's why I can't use FireFile - because I am not allowed to create an account and register my website?
Thanks for clarifying what's going on, and how can I fix it?