Can you try this in a clean profile? Instructions on how to do this can be found here:Use the Profile Manager to create and remove Firefox profiles

The new tab page works correctly with a fresh profile.

Curiously the default profile still does not work after I disable all plugins and add-ons.

Now, try following the instructions in Back up and restore information in Firefox profiles, following the instructions for restoring to a different location. (The different location being the new profile you created earlier)

Let me know whether this fixes your problem or not.

So I will overwrite my default profile with all my plugins, add-ons, bookmarks, and preferences with the new, blank profile?

That will certainly fix the problem the the new page tab, but will I loose all my current plugins, add-ons, bookmarks, and preferences?

No, transfer the data from your old profile to your new one. That way your old profile is still intact, and the new profile has your information. OR, it's easier to just do Firefox Reset. Start Firefox using your old profile, and Reset it. Refresh Firefox - reset add-ons and settings

Restoring the contents of my default profile folder to a fresh profile folder did not work.

Here are the steps I took:

1. Closed Firefox and started it up again with "firefox.exe -p"
2. Created a new profile called "TEST SETTINGS"
3. Navigated to "%APPDATA%\Mozilla\Firefox\Profiles\ "
4. Opened up my "abcdefg.default" profile folder, selected everything with "CTRL+A" and copied it all with "CTRL+C"
5. Opened up my "tuvwxyz.TEST SETTINGS" profile folder, deleted all the contents of the folder, and then pasted the contents of my default profile folder.
6. Opened Firefox with "firefox.exe -p" and selected the new "TEST SETTINGS" profile
7. The new tab page still does not function properly.

As an aside I noticed a large section in Firefox's Troubleshooting Information titled "Important Modified Preferences" (It is attached to the "More system details..." line in my first post; the forum seems to have eaten the formatting though). Would one of those preferences break the new tab page?

Found the issue:

dom.storage.enabled apparently affects the new tab page behavior (bozhe moi!)

I had mine set to false; this apparently breaks the new tab page. Changing back to true restored the expected behavior.

It would be nice if the About:Config entries at http://kb.mozillazine.org/ included a cross-indexed description of how changing those various options will affect/bugger up features in Firefox. (And while I'm wishing I'd also like 1 million dollars, a pony, and world peace). C'est la vie...

Thank you for you help crazyskeggy and Tylerdowner

Changes made on the about:newtab page are stored in the chromeappsstore.sqlite file in the Firefox Profile Folder under the pinnedLinks key and blockedLinks key.