@reasoning logic,
Do you have a dictionary installed and selected?
You can see which dictionary is selected if you right-click in a text area and open the Languages submenu. At least one dictionary should be installed and have a check mark to indicate that it is selected.
Open the "Add Dictionaries" link to install a dictionary if you do not have one.
Make sure that [X] "Check Spelling" in the right-click context menu is check-marked.
You can enable or disable spell checking globally:
Tools > Options > Advanced : General: Browsing: "Check my spelling as I type"
You can look here for dictionaries:
https://addons.mozilla.org/firefox/language-tools/
You can check for problems with preferences and try to rename or delete the prefs.js file and possible numbered prefs-##.js files and a possible user.js file to reset all prefs to the default values.
http://kb.mozillazine.org/Preferences_not_saved
http://kb.mozillazine.org/Resetting_preferences