Douglas:
As SlackAlice has indicated, your PC might see the security certificate on the Hotmail site as having an invalid security certificate and, again as SA states, by far the most common cause is that the date is incorrectly set on your PC. (Hover your cursor over the clock, at the bottom right of your screen to see the date on your computer. If it's wrong, right-click on the clock and select 'Adjust Date/Time. If it keeps going wrong you'll need to replace the BIOS battery in your computer).
RSVP:
Make a note of any extensions that you're using with Firefox which you wish to keep (Tools > Add-ons > Extensions). Go to Help > Troubleshooting Information and click on 'Reset Firefox'. Then reinstall the extensions.