Create a new profile as a test to check if your current profile is causing the problem.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

In cases where this is caused by a certain known bug affecting the location bar the current recommend solution is to rename the file places sqlite if using the addon places.maintenance does not work

• https://addons.mozilla.org/firefox/addon/places-maintenance/

I know it seems odd having an addressbar problem and being told to look at fixes to problems in the bookmarks database This is not something to do normally because you lose history information, but renaming rather than deleting the database gives an option of reversing the procedure.

See also

• http://kb.mozillazine.org/Locked_or_damaged_places.sqlite#Rebuild_Places_database.
• With steps to take explained in full in
  Firefox 39 address bar not working /questions/1070999#answer-750702 along with a note about an advanced method, that may restore the database including History