You could try backing up your regular profile, then creating a new profile and copying the file prefs.js from that new profile to the old. That should clear all settings but should also make Firefox unaware of any config values changed or added by extensions. If that process does not resolve the issues you've been having you could restore the prefs.js file from the backup. If it does resolve them, you can reinstall any extensions you want to continue to use.
Sounded promising, tried that, but no success - personal settings have no effect. Also removed all addins and extensions - no success. So I tried the following, in the hope that I can keep my old profile and not break my syncs:
1. Created new profile and copied personal files of broken profile to new profile - success (as stated previously)
2. Overwrote broken profile with ALL original top folder files of new profile: partial success. When I open Paypal, I see the top menu. Then I open Idealo, but no pictures, and in Google the Login buttons don't work. HOWEVER, if I change the opening sequence of these three webpages, always the FIRST webpage works, but the other 2 after that don't.
So I felt lucky and copied all personal files from a backup broken profile to the mixed broken profile in 2, and suddenly everything works!
So, since a new profile has 40 top files, the broken profile has 95 files, and neither extensions, addons, bookmarks, pinned webpages, cache, security databases, private settings or any other personal files seem to have caused the problem, it must be one of those 30 or so other non-personal files that somehow got installed by Firefox over time.
Thanks guys for your help - maybe someone can figure it out...