If you copy/paste a full Google URL into the private window address bar, is it also unable to load?

Minimal: https://www.google.com/search?&q=firefox

URL From Firefox's Search Bar: https://www.google.com/search?q=firefox&ie=utf-8&oe=utf-8&client=firefox-b

I don't think this is a problem with Firefox's Tracking Protection feature, but to double-check, you could turn that off using the steps in this article: What happened to Tracking Protection?.

Assuming that makes no difference, I would suspect an extension. You didn't share a list with us, so I'll let you take the first crack at trying to figure out which one it might be.

You can view, disable, and often remove unwanted or unknown extensions on the Add-ons page. Either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

In the left column of the Add-ons page, click Extensions. Then cast a critical eye over the list on the right side. Any extensions that Firefox installs on its own are hidden from this page, so everything listed here is your choice (and your responsibility) to manage. Anything that filters content (e.g., ad blocker, tracking blocker, privacy filter, etc.)? If in doubt, disable or click the Options button and see whether it has options related to regular vs. private windows.

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

Any improvement?

Maybe do a malware check with several malware scanning programs on the Windows computer.

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware

Please scan with all programs because each program detects different malware. All these programs have free versions.

Make sure you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender:
  http://windows.microsoft.com/en-us/windows/using-defender
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked

I ran a scan with both Avast and Malwarebytes (using their free versions) before asking for help. There was a section I filled out while submitting my question that asked about extensions, I think that can be found in the side tab "Question Details"

I also just restarted firefox and the problem hasn't come back, so I'm not sure if something happened to affect it. I'm going to have to backtrace my steps before discovering the problem to see if it had anything to do with an active login, which is the only thing I can really think of with my limited IT knowledge that may have been the cause, since it worked in the normal browser and on other computers I have available.