I would recommend trying to start Firefox in Diagnose Firefox issues using Troubleshoot Mode to see if this fixes the problem. If so, it may be some add-on causing the problem.

A machine with those specs (you don't mention CPU speed/type, but that can't be too bad either I guess) sould never be more than a few seconds about starting Firefox.

Also please see our Use the Troubleshooting Information page to help fix Firefox issues article and post this information too, this may help us help you identify the problem.

Please let us know how above works out, and if we can be of further assistance. Detailed feedback is appreciated and helps us to help you better, plus enables us to better help other users with similar issues.

A possible cause is security software (firewall) that blocks or restricts Firefox without informing you about that, maybe after detecting changes (update) to the Firefox program. Remove all rules for Firefox from the permissions list in the firewall and let your firewall ask again for permission to get full unrestricted access to internet for Firefox. See Configure firewalls so that Firefox can access the Internet and http://kb.mozillazine.org/Firewalls