Firefox can lie about its identity, if set up that way. You can use this test page to see what it is telling my site (it's the text in red):

https://jeffersonscher.com/res/jstest.php

Normally it would say something like this for Windows 7 (64-bit):

Mozilla/5.0 (Windows NT 6.1; WOW64; rv:40.0) Gecko/20100101 Firefox/40.0

If a strange user agent is caused by a Firefox setting, this article should help in clearing it: How to reset the default user agent on Firefox.

It also could be caused by an add-on, most likely an extension.

Some unexpected update messages can indicate a bad add-on or other malware. If this issue is not resolved by the first part of this response, here's my suggested procedure for tracking down and cleaning up bad add-ons, hijackers, and ad injectors. I know it seems long, but it's not that bad.

(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. Bear in mind that all extensions are optional, none come with Firefox, and you can learn more about them by checking their reviews on the Add-ons site.

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.

Success?

(4) Check your connection setting here:

"3-bar" menu button (or Tools menu) > Options > Advanced

Click the Network mini-tab, then the "Settings" button. The default of "Use system proxy settings" should piggyback on your Windows/IE LAN setting, or you could try "No proxy" to see whether that helps.

Note that you posted with a Google Chrome 23.0 user agent on Windows 7 (NT 6.1)

• User Agent: Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.11 (KHTML, like Gecko) Chrome/23.0.1271.95 Safari/537.11

See:

• https://support.mozilla.org/kb/Finding+your+Firefox+version
• https://support.mozilla.org/kb/websites-say-firefox-outdated-or-incompatible

Thank you both for this valuable information. First, I opened about;config in Firefox and noticed the general.useragent.override was showing the parameters initially seen in the JS Browser Test page. I reset it and once again opened the about:config and now it shows Firefox 40.0 and Windows 10 (64), which is correct. I do not see these little windows anymore and I can now get to the Keep Your Firefox Healthy page. Thank you again!!