Sometimes Addons cause for problems ,so first you check whether the Find option works after disable the all addons.To do so you have to follow these steps : open menu > open help menu > Restart with add-ons Disabled Now this pop up comes up Are you sure you want to disable all addons and restart the firefox Click on Restart and in a second you get one more pop up which says reset firefox or open firefox .

open firefox and then check again whether find shortcut key works or not .

See this thread for more details about Reset Firefox

Make sure that the "Match case" box doesn't have a checkmark.

Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem.

• Switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance
• Do NOT click the Reset button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Separate issue;

Your System Details shows;

Installed Plug-ins

Adobe PDF Plug-In For Firefox and Netscape 11.0.07 Adobe PDF Plug-In For Firefox and Netscape "9.5.5"

Having more than one version of a program may cause issues.