Chrome Version 45.0.2454.85 m.
All of a sudden one day Inspect Element option in right button context menu greyed out. Ctrl + Shift + I doesn't do anything and F12 doesn't do anything. Cleaned the cache as suggested by one answer here but that didn't help either.
I found out that for strange reasons, either Windows update or Chrome update changed this registry setting.
Software/Policies/Google/Chrome/DeveloperToolsDisabled to 1. Changed it to 0 and restarted the system.