The serial number is usually found on a sticker that is stuck to the back of the installation instructions that come in the box. At least for me, the serial number was 32 digits/letters long. It should probably be around that length for you, too.
If you have FCE 4 the serial number will probably be formed by a single letter followed by 9 groups of numbers or letters in threes, followed by a group of 4 mixed numbers and letters.
This is a made up example to show you how the numbers and letters
might look ........ you won't usually find lots of consecutive series of letters and numbers in a real serial:-
I've tried everything from with and without dashes, the 1's replaced with capital i etc. As of now nothing seems to help. Time to give the Apple Office a call?