I've never heard of that problem. I recommend uninstalling Firefox (save your preferences during uninstallation), downloading the newest version of Firefox, and installing from that fresh installer.

To uninstall Firefox, press the Windows key and R simultaneously to open the Run dialog, type C:\Program Files (x86)\Mozilla Firefox\uninstall\helper.exe, and click OK.

Download the newest version of Firefox from here after that and install it.

Does this solve the issue?

Grab the full off-line installer package from here: http://www.mozilla.com/en-US/firefox/all.html

As long as your current installation is installed in the default location, I don't think you'll have a problem with installing Firefox 30 over your current installation.

But to play it safe, it's not a bad idea to backup your Profile, just-in-case. https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

That's not a bad idea, but that's probably the problem. They're attempting to upgrade from 24 to 30. That's a significant upgrade, and the upgrader probably can't handle it. It would be way safer if they completely uninstalled it.

You, no, that's wrong. The update from 24 to 30 is a totally safe upgrade, you don't need to uninstall.

A Simple pave over installation will be more than enough.

You have a point, but the problem could be anything. Malware, incompatible addons, lingering processes, or basically anything can halt an upgrade. Upgrades are not foolproof.