QT on it's own won't cause the problems you describe. The system file itself may be corrupted( as a result of a QT crash) leading to a reinstall of the OS(unless you have a saved copy of your system folder handy), I'm afraid. Because QT is so deeply integrated, serious crashes can have significant and wide-reaching side effects. To thoroughly replace QT you MUST first remove all previous trace of it, EVERYTHING! Nuke the site from orbit - it's the only way to be sure, and so forth. Look wider than just QT at this stage.
I'm puzzled by one thing though, is this browser only or just using the QT player on it's own? Have you ever installed Maczilla? or Hack TV, either of those would've been a mistake!!!