I would of guessed not without knowing the algorithm used to generate the key, time to get your reverse engineering hat on!
Work out what kind of hash/encryption is used first, and then I don't know, use the date+time+MAC_ADDRESS+MoBo_Serial# and see what you come up with etc etc
Its going to be a long winded and almost impossible method of doing it. Instead you might want to try to reverse engineer the software that generates the key, then you can work it out. This is a much more realistic solution.