I can be of no help, because you have a very extreme problem. Nothing even remotely close to what you describe, ever happened to me. And, I have an old computer, where all sort of things could go wrong. I am not sure what is your OS, but it is, certainly, newer than mine.
I don't know if add-ons could cause problems like yours. You can, always, try to start in Safe Mode. The fact that some add-ons are incompatible is irrelevant.
I have kept a copy of Firefox 3.6.x, with its own profile, just to check for possible weirdnesses, but the behavior of 3.6.25 and 9.0.1 is alike.
UserAgent: Mozilla/5.0 (Windows NT 5.1) AppleWebKit/535.7 (KHTML, like Gecko) Chrome/16.0.912.63 Safari/535.7