Hmmmm ... first, Final Cut Studio doesn't "start up" at all. It is a package of applications that include Final Cut Pro, DVD Studio Pro, SoundTrack Pro, Compressor, Cinema Tools, and Qmaster.
Each of the individual applications should start up normally - IF you upgraded correctly.
But before we get too far into diagnosing your problem, it would help to know what kind of Mac you have, what version of OS X you're running and what version of FCS or FCP you have.
It would also help to know just what the error message you receive actually says. Remember, we're not mind readers and we aren't there looking over your shoulder. Provide as much detail as possible.