Upgraded to FF3.5.x: initially, only problem was several extensions (Tab Mix Plus, Personal Menu) wouldn't work. Rebooted/restarted, but not only didn't help, FF itself wouldn't run (at all). Uninstalled/reinstalled both FF 3.0.x and 3.5.x, rebooted PC -- no joy. Noticed that with Task Manager open, trying to boot FF was followed by a brief (2-3 seconds) appearance of process "firefox.exe" but promptly disappeared. Running FF Safe Mode didn't work; rebooted Windows in Safe Mode, but FF still wouldn't launch. Was able to start Profile Manager, but button for New Profile didn't function.
Your installation seems to be corrupted.
Then, do a fresh install.
Checking that a portable edition works fine is also a good idea.