Im not sure about serial number but you can take off your battery cover and check there. I think your model number is in the settings under "About Device" or something like that. Go into settings and scroll to the bottom. Hope you find it.
I purchased one from CraigsList (You won't believe how cheap they are on CL).. and registered on the perks site. I had my code in my inbox before I could even pull GMail up on the computer.