Well, after installing Firebug, he asked to restart Firefox, and this was done, but for some reason, the reboot did not help to make the net tab. So I quit Firefox and restarted again, and now it works.
even after a restart, FB Connect seems to suffocate again. Restarting worked again ... more details later ... it seems like this is the way to solve it for now - it's just restarting it.
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