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The problem must be with some components of Final Cut Studio. First, delete the old preference files of FCP. Goto Macintosh HD > Users > your username > Library > Preferences
folder and trash the file com.apple.finalcutpro.plist file.
Then trash the folder Final Cur Pro User Data
Then Insert the Final Cut Studio disc to your Mac, once it loaded open the 'Install Final Cut Studio' file. Click Continue, then Continue, again Continue and then click Agree. Select the destination disc. Then Enter Name, Company, Serial Number (if asked) and click Continue. Then in the Custom Installation Screen, select Final Cut Pro and uncheck all other applications, then click Continue and install it. See picture below;
Please let me know how it goes...