If Final Cut Pro will not accept the serial number as it is entered, verify that the last four characters are "-340" (dash, three, four, zero) at the end of the serial number. It these any of these numbers are missing, please add them so that Final Cut Pro will correctly recognize the serial number as valid.
Also, make sure that you are not attempting to use the serial number for the QuickTime Pro upgrade that is also a part of the Final Cut Pro package. Additionally, be sure that the characters you enter are the same as the ones on the label. For example, don't confuse the letter "I" with the number "1", or the number "0" with the letter "O".