In order to change the default search engine or the order of search engines in the top right search box in Firefox, please perform the following steps:

1. Move the mouse cursor inside the search box at the top right of the Firefox window and click the down arrow next to the provider's logo.
2. If you would like to select another search engine, simply pick the engine from the dropdown list.

In order to change the order of the search engines, do this:

1. From the dropdown list, select Manage Search Engines....
2. In the upcoming window, you have all your search engines listed. To change the order, simply click one search engine and then select Move up or Move down from the buttons on the right side in order to change the order of the search engines.

The problem is searching with the location bar. Not the search bar.

It's normal for a one-word "search" to be tried as a domain. By one word, I mean a string that does not have any spaces in it, whether it's intranet or mozilla.org or any other string with no spaces.

When Firefox gets a response that a site does not exist, it should then throw the query over to Google. That's what happens if I try jcrew.

Do you get a white error page or do you get something from your ISP / DNS service provider? Some ISPs / DNS service providers take the liberty of giving you their own search results page instead of a standard error, so Firefox never ends up sending the error to Google.

Easiest to make sure that you do a search is to use a (one letter) keyword search (g cats).
You can add a keyword to installed search engines via "Manage Search Engines" in the search bar drop-down list or create a bookmark and add a keyword to this bookmark in the Bookmarks Manager (Library).