A 1x1 pixel image usually is a tiny, transparent dot (GIF format images are easily made transparent) used to track visits to a web page. If the page is stuck loading a single-pixel GIF it could indicate a problem with that web site, or it could be that your security software/add-ons or content filters are blocking that page.

To see whether an add-on might be involved, you could try re-doing your search in Firefox's Safe Mode.

First, make a backup of your computer for safekeeping. To back up Firefox, see Backing up your information.

Next, try starting Firefox in Firefox Safe Mode. Be careful not to "reset" anything permanently if you didn't back up.

Do the links work normally? In that case, you could disable all your non-essential add-ons and experiment until you find the culprit.

Thank you, jscher2000, for posting this answer to my question, and I'm sorry I've taken so long to reply.

Yes, it was my security software. I found out that .GIF files are very commonly used for internet graphics, particularly animations and ads. I use Kaspersky Internet Security. I had the anti-banner setting enabled, which stopped the display of .GIF files. I'd rather not see all the ads, but I've found I can very easily disable the anti-banner setting to view a particular page and then enable it again to avoid the ads when I read the news. There aren't that many pages that are entirely made up on .GIF files.

Again, thanks muchly!