That is very disturbing!

This appears in place of the new tab page or as an additional page?

Here's how you can check/change your new tab page:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste newtab and pause while the list is filtered

(3) Double-click the browser.newtab.url preference and enter your preferred page:

• Page thumbnails (default) => about:newtab
• Blank tab => about:blank
• Built-in Firefox home page => about:home
• Any other page => full URL to the page

Press Ctrl+t to open a new tab and verify that it worked. Fixed?

If problems persist: some potential diagnoses and remedies:

If Firefox won't let you edit this setting: you may have something called SearchProtect on your system. This needs to be removed from the Windows Control Panel. If the status says "locked" we will need to help you investigate an "autoconfig" file.

If Firefox lets you save your change but ignores it: one of your extensions may be overriding it. You can review, disable, and/or remove extensions on the add-ons page. Either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then cast a critical eye over the list on the right and disable (or remove) anything unknown.

If the change works during your session, but at the next startup is back to the unwanted page: you might have a user.js file in your personal Firefox settings folder (your Firefox profile folder). This article describes how to track down and remove the file: How to fix preferences that won't save.

Any luck?

And/or, let's tackle the malware-ish aspect of this first. Here's my suggested procedure for tracking down and cleaning up bad add-ons and other hijackers. I know it seems long, but it's really not that bad.

(For Windows Vista, 7, 8, 8.1; XP is somewhat different)

(1) Open the Windows Control Panel, Uninstall a Program. After the list loads, click the "Installed on" column heading to group the infections, I mean, additions, by date. This can help in smoking out undisclosed bundle items that snuck in with some software you agreed to install. Be suspicious of everything you do not recognize/remember, as malware often uses important or innocent sounding names to discourage you from removing it. Take out as much trash as possible here.

(2) Open Firefox's Add-ons page using either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons
• in the Windows "Run" dialog, type or paste
  firefox.exe "about:addons"

In the left column, click Plugins. Set nonessential and unrecognized plugins to "Never Activate".

In the left column, click Extensions. Then, if in doubt, disable (or Remove, if possible) unrecognized and unwanted extensions. All extensions are optional; none come with Firefox.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Any improvement?

(3) You can search for remaining issues with the scanning/cleaning tools listed in our support article: Troubleshoot Firefox issues caused by malware. These on-demand scanners are free and take considerable time to run. If they finish quickly and especially if they require payment, you may have a serious infection. I suggest the specialized forums listed in the article in that case.

Gosh, I really appreciate all your suggestions! I will give them a try tomorrow. I think your malware idea is a good one. I have been a Firefox user for years and this is the first time this happened!

I'll let you know how I make out tomorrow.

This is often the result of Flash cookies, also known as LSOs. Flash cookies can be automatically deleted with the Firefox extension: Better Privacy"

https://addons.mozilla.org/en-US/firefox/addon/betterprivacy/