Quartz extreme is to do with the graphics card. I think it was FCP5.1 that this problem started with. It does a check to see if you've got the right hardware. If not, bye bye.
There is a hack you can do to force the check to look for the graphics card you actually do. Basically, what you do is remove the startup check from the application package contents. This, of course, is delicate work, so you should always make a copy of the files you are going to be stripping beforehand.
I don't know exactly what you would be looking for, but basically a string that mentions minimum system requirements and quartz.
Google would probably be helpful.
OR, run an earlier version of FCP.