Try Firefox Safe Mode>Hold down Shift key as you double click on Firefox icon. Don't check any boxes.

Try temporarily disabling your anti-virus and your firewall.

Report back.

Tried that and it still won't load. It got as far as the prompt that has all the boxes. After that, nothing happened.

I should also point out that when I reinstall it, it does a compatibility run on some add-ons, and when it does so, it inevitably freezes.

Did you click on "Continue in Safe Mode" to actually run Firefox in Safe Mode? See the Diagnose Firefox issues using Troubleshoot Mode article.

See also Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems for next steps, whether or not Firefox runs in Safe Mode.

Still not working. Am I just going to have to resign myself to using an older version?

If you are working in a a corporate situation - Is anyone around you using Fx4 successfully? If Firefox is permitted you should ask your administrator to make sure Fx4 is cleared by your firewall.

With many "domestic" firewalls you need to give new permission for new versions.

You'll notice in Alice Wyman's article that you can try a version of Safe Mode(I'm not sure whether it disables Hardware Acceleration) if you can get to the first page(after closing down any firefox running via Task Manager) you can try >Firefox orange button >Help >Restart with Add-ons disabled. Then you try her other suggestions.

After that you would probably need to do an uninstall/re-install and try a new clean profile.