To solve the problem is a bit of a chore, let me explain, since the problem only occurs in your User account the problem file is in your home folder.
Settings are almost all in your Library folder and the most likely folder is the Preferences (settings) folder inside the library folder.
Now to find to conflict is a bit of a process.
Since you can not change things inside your Library folder when you are logged in you need to do this from another User, but the best way is the root user, yours is most likely not active yet so first you have to activate Root.
How to enable the root User:
Open /Applications/Utilities/Directory Utility
Next click the padlock
Enter password
Now under the Edit in the Menu Bar click enable root User.
It will ask for a new password to be set(twice)
Logout
You now get to the login screen and see other, click on that and enter root as name and the password you entered earlier.
Open a browser and download Show & Hide, this is a small application which makes your invisible files visible, download here.
http://www.longfingers.com/download/Show&Hide.zip
Unzip, click it and make your files visible.
Now, navigate to Your normal User Accounts home folder and locate the /Library/Preferences folder, rename it to Preferences Old(Or whatever you want.)
Logout, and login to your normal User Account, everything (settings) are now reset but don't worry they are in Preferences Old.
There is a new Preferences folder now with new setting.
Open Firefox, is it working now??????
If so, the problem file is in the Preferences folder.
In this case logout and login into root again, now drag half(50%) of your files from Preferences Old to preferences.
Logout of root and login to normal User account.
Open firefox and try again.
Problem still gone, the 50% files are Ok and the problem is in the other 50% in the Preferences Old folder.
Problem is there, the problem is now back to the preferences folder.
So, in essence you have to each time half the files and eventually you'll find the one file which is the culprit.
It is a bit of a job though.
If the problem didn't go away by renaming the preferences folder to Preferences Old the problem is in another folder, the next one would be Application support.
You can revert back to the old situation by renaming the old folder back.
For security I would make a copy of the folder you work on and place it in a safe place like a USB stick or just on the desktop.
Now, question, do you understand the procedure, if not I can make a few screen shots.
Screen shots would be great! So last night the website worked under my other account and now today it's doing the same thing as my regular account.... ??