Click on the Firefox button on the top left corner > Options > click on Navigation Toolbar

I already had the Navigation toolbar on. I tried turning it off and on again, but am still unable to enter addresses into newly opened tabs except addresses from the Bookmarks section.

The problem has not been solved.

Try the Firefox SafeMode to see how it works there.
A troubleshooting mode, which disables most Add-ons.
(If you're not using it, switch to the Default Theme.)

• You can open the Firefox 4.0+ SafeMode by holding the Shft key when you use the Firefox desktop or Start menu shortcut.
• Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.
  

Don't select anything right now, just use "Continue in SafeMode."

To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut (without the Shft key) to open it again.

If it is good in the Firefox SafeMode, your problem is probably caused by an extension, and you need to figure out which one.
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes

When you figure out what is causing that, please let us know. It might help other user's who have that problem.

Thank you - Safe Mode worked.

The problem appears to be the Google search bar takes over the space where the URL is entered, and comes up with search results instead of entering the web site.

Your input much appreciated.