You would probably have to close the tab that is causing this hang.
So you can try to middle-click this tab to close that tab if you have a clue which one is causing it.

See also:

• Tab Permissions: https://addons.mozilla.org/firefox/addon/tab-permissions/

If I could close the offending tab, I would do that and there would be no problem. The problem is that a script running in one tab has hung firefox entirely so that I cannot take any actions through firefox, such as closing the tab in question by clicking on the "X". At that point, nothing in firefox works and the only way out is to kill the firefox process/PID from Windows, or if a message comes up that firefox is not responding, then take the action to stop it. In any case stopping firefox entirely is what I am trying to avoid: it's like having to reboot the OS because one lousy process is causing a problem. What one would ideally like to be able to do is to kill the specific instance of the script (presumably javascript) from outside firefox, which might cause the specific tab to die, but not all of firefox. I generally know what tab is causing the problem because that's the one I'm working in, doing something and then it hangs. 98% of the time when it happens it's the "active" tab. It seems to me that one tab ought not be able to hang firefox entirely, just as one application's process should not be able to hang the OS entirely, and at least there ought to be tools or a method to deal with it without stopping firefox completely.

Sorry if I misunderstood your question, but am I right in that you have your tabs automatically load when you start Firefox? Maybe you could try disabling the option that loads all tabs when you start the browser. The JavaScript won't load until you click on the tab it's in. If you can't do it at the moment because it's hanging Firefox before you can change it, try disconnecting yourself from the internet temporarily (you'll also be able to close the tab this way) and changing the option then.

The option to disable tabs to load automatically is in Tools -> Options -> Tabs.