Sounds like there could be more than just Firefox causing a problem here - especially if you've re-installed it. Have you manually cleared the cache and browsing history? Could be some cached ad-related file thats casuing the fault.

Have you tried using Ad-blocking plugins like No-Script and AdBlock Plus ? These are freely available through the Addon channels - personally can't live without these enabled to block the ads on sites for bandwidth conservation alone.

If this fails, I'd suggest running a MalwareBytes AntiMalware scan, and even a Spybot Search and Destroy scan on the system too.

I completely removed all settings, included the profile. I installed the suggested plugins, so I will have to follow your other suggestions. Thanks for helping me out!

New observations:

When starting up FF asks whether I prefer a new session or restoring the old session. Both are the same site. Still restoring works, but building a new session makes FF collapse.

Even clicking this site form 'history' makes it collapse, while clicking the link from notifications@support.mozilla.com works fine.

Scripting seems to be the problem: With No Script I disabled some and the exiting grows lesser and lesser . . . Troubles were caused by Google related scripts.