A Google search here of new.tab not and looking at 6 of results shows 5 of 6 report ask.com toolbar extension at fault, and 1 of 6 report FoxTab extension at fault.

ask.com can be difficult to remove, see

• Problematic extensions - MozillaZine Knowledge Base
  http://kb.mozillazine.org/Problematic_extensions
• Uninstalling toolbars - MozillaZine Knowledge Base
  http://kb.mozillazine.org/Uninstalling_toolbars

FoxTabs also causes black screen

• https://support.mozilla.com/questions/840090

Thank you for getting back tome on this!

So, if the feature still works when I'm in Internet Explorer...? Would that suggest more that the FoxTab extension is at fault?

Firefox extensions do not affect Internet Explorer. Your problem was in Firefox did you have either of the two extensions and disable them if you did. In other words was your Firefox problem solved by disabling an extension (and which one), or are you still unable to open a tab in Firefox.

If you saying you like ask.com and are using it in IE and wonder why it doesn't work in Firefox -- I don't know, two different browsers. If there are more serious problems elsewhere because of ask.com -- I don't know, I would avoid something that is installed as crapware when you install something that you do want.