Started with Firefox 4.0 install. Google toolbar option settings have no effect. Won't automatically search from search drop down list. Also won't suggest searches as I type. Darn thing won't even fill in the search bar from the drop down list. I've been in the business for 25 years doing everything from computer design to application software. I don't expect x.0 of anything to be perfect. However, this problem should have been caught in test/validation. Or, maybe Firefox users are the test/validation team. If that's the case, then I need to get paid. Running Vista SP2.

Try uninstalling the Google Toolbar extension and installing a fresh version of it.

The URL address box does offer helpful completion of search words but only as to previously visited web sites. If I switch from Google search to another search engine in the search box, not eve suggested completions to the search. What gives here?

Are you talking about an issue with the Google Toolbar extension's search bar, or not?

If so, can you navigate the "suggestions" with the up / down arrow keys on the keyboard, and then make you selection with the Enter key?
If so, the fault is with the Google Toolbar extension and users have said that uninstalling it and reinstalling the GTB extension fixed that problem.

If you are looking for restoring the Google "I'm feeling lucky" search feature to the Location bar (URL bar) in Firefox 4.0, try this extension.
https://addons.mozilla.org/en-US/firefox/addon/luckybar/

I performed a remove and re-install of the Google toolbar. That didn't help. Also tried to find an earlier version of the toolbar. Foxfire blocked installation and said it wasn't compatible with Firefox 4.0. The search engine function in the Navigation toolbar works just fine. Part of the problem is I'm not certain what's at fault. The switch to Firefox 4.0 forced a Google toolbar update. I'm trying to avoid downgrading to Firefox 3.6.

Ok, so I punted. Using the Firefox View->Toolbars->Customize functions I removed the Google search window (which wouldn't search from drop down list) and replaced it with the Navigation search window that behaves properly. Problem hidden, but not really fixed. When the next version of Firefox or Google toolbar rolls around I'll check and see if things are any better.

Darn. The Navigation toolbar doesn't save the search history, so it's not a true replacement for the Google toolbar. Still searching (no pun intended) for a fix or kluge for this problem.

This worked for me, FF 4.0: I removed the Google search box (Tools, Add-ons, Extensions, remove) then "reinstalled" with a right click of cursor while in menu bar, then "customize" and drag the Google search box to where I wanted it.