I have lost my OS x installation disk and now need my 11 digit serial number. What can I do?

Hi, I have not used this PC for a while and decided to set it up for my daughter. I had forgotten my password so went into single user mode and try to override this. Unfortunately after a reboot I was taken back to the "Welcome" screen and now I need my 11 digit serial number to continue. Unfortunately I have lost the installation disk that came with the machine and I am now stuck! Any help please??