So, will Firefox just not open, or what exactly happens?

Try opening up Internet Explorer, going to www.getfirefox.com, click the big "Download Now" button. Then, click run. Install Firefox on your machine over your old install. This is just to make sure none of the components of Firefox are broken. All your old information will be saved.

Then, try to restart your PC and reopen Firefox. Does it work? If not, try starting it in Diagnose Firefox issues using Troubleshoot Mode. It is works there, it is likely that one of your extensions is broken. Read How to disable extensions, Personas, and plugins, and disable them one by one until you find the culprit.

A possible cause is security software (firewall,anti-virus) that blocks or restricts Firefox or the plugin-container process without informing you, possibly after detecting changes (update) to the Firefox program.

Remove all rules for Firefox and the plugin-container from the permissions list in the firewall and let your firewall ask again for permission to get full unrestricted access to internet for Firefox and the plugin-container process and the updater process.

See:

• https://support.mozilla.org/kb/Server+not+found
• https://support.mozilla.org/kb/Firewalls