Hi p452833, I can think of two other things to check:

(1) Has the built-in Google search plugin been replaced with a different one?

You could try the "Restore Default Search Engines" button below the One-Click Search Engines box on the Options page, Search panel, if it's not grayed out.

If you now find two Google plugins, try the other one.

(2) Could a privacy add-on or external filter be blocking the suggestions?

You could try testing in Firefox's Safe Mode:

In its Safe Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to help you assess whether these are causing the problem.

If Firefox is not running: Hold down the Shift key when starting Firefox. (On Mac, hold down the option/alt key instead of the Shift key.)

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" Help > Restart with Add-ons Disabled
• (menu bar) Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any improvement?

Hi jscher2000:

I tried the first of the solution, and went to the "search" page of the "options" in the "open menu", all the search engines (Google, Bing, Amazon, Duckduckgo, ebay, twitter, and Wikipedia) were checked, so I un-checked all but Google, IT WORKS, but after that, I re-checked all previous un-checked search engines (return back to the original state), it still works,

Hi p452833, that's a bit like turning it off and turning back on again. It often works but we'll never know why it was broken. I won't worry about it if you won't.