From your "More System Details" it looks as though you have the versions listed on Norton's recent update announcement site:

http://community.norton.com/t5/Product-Update-Announcements/Firefox-31-Support-for-Norton-Toolbar/ba-p/1155994

When I check the Norton forums for this issue, I don't see a solution or official comment:

http://community.norton.com/t5/Norton-Toolbar-Norton-Identity/SafeWeb-icons-AWOL-Again/td-p/1156546

If this is a deal breaker for you, and you prefer the security trade-off of downgrading Firefox, see this article: Install an older version of Firefox.

If you don't mind a little more troubleshooting, could you check the Browser Console for any error messages that might be relevant? Here's the sequence I suggest:

(1) Run your Google search

(2) Open the Browser Console using Ctrl+Shift+j (or "3-bar" menu button > Developer > Browser Console)

(3) Click the Clear button

(4) Switch back to the browser and reload the search results page

(5) Check the Browser Console for errors (you can temporarily hide log entries and style warnings by clicking those buttons on the top bar)

Anything indicating an add-on failure or blocked function?

Thanks. I tried exactly what you said (though wasn't entirely clear whether clicking on the top buttons would filter out rather than in). I scrolled through the list and didn't see anything re. an add-on or blocked function. Note that there were a number of java errors but I have java disabled since even though I keep it up to date it's still a major security risk. I don't disable it in the browsers directly, but in the java console itself. I noted earlier it's only Google searches that don't display the Norton icon to the right of the results. Actually it happens with ALL search engines EXCEPT Norton's own (which is a subset of Ask, but using Ask alone instead of through Norton also is missing the Norton "N" icon to the right). No problem with Internet Explorer or Chrome, and there was no problem before the Firefox 31 upgrade. I've also since tested on 2 of my Windows 8.1 machines and they have the identical issue as my Windows 7. So there's definitely a bug in Firefox 31 in combination with Norton Internet Security!

Thanks for checking. I should note that there is a difference between Java and JavaScript. The Java plugin is used on a few sites to run applets. JavaScript is used on nearly every site these days, and is interpreted directly by Firefox. The console has a mishmash of script errors from add-ons and the page, so it can be difficult to interpret.

Maybe I can get a 30-day evaluation of Norton and try it out...

You should be able to get an evaluation version of Norton. Make sure it's Norton Internet Security, NOT 360, or Norton One (though I suspect the problem would exist with those as well). When you install Norton make sure to enable all Web settings, then keep forcing live updates until the product is completely up-to-date. Then make sure your Windows is up-to-date. Then make sure to enable all Norton add-ons in Firefox. It may take several opening/closings of Firefox until the Norton toolbar can be enabled. You'll have to answer some Norton questions about allowing along the way. Do NOT let it make Norton the default search (I always use Google as the default). Once you can see the Norton toolbar try running a Google search. Then try the same search using Norton's toolbar for its Safe Search. With Norton results you should see a green or red "N" to the right of each results. Green means safe, red unsafe. Click on the "N" provides more results. With Google or other search sites the "N" is missing altogether.

Sorry I haven't gotten around to trying this. Since I already have paid security software installed, it's a bit of a chore to test another program.

That's ok. I've since checked it out on another Windows 8.1 machine and the same thing. Norton worked properly with 30 and as soon as I upgraded to 31 the "N" disappeared from Google and other searches. I ran all Norton and Windows updates, still no good. That makes 3 machines. Mozilla needs to fix this or else I'll stop using Firefox since the Norton feature is essential.