It is possible that your security software (firewall, anti-virus) 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.
I do not seem to have any rules listed for Firefox within my Firewall.
Previous to today, I was running Firefox 19 and I had the same issue. I downloaded the version 22 on a different computer, saved it to a flash drive and installed. The issue remains, and hence the opening of this thread. I have reviewed and abided by the links you supplied, however, I cannot seem to find proper resolution.