The location of your AMD processor's serial number may vary, depending on its type and model. In most cases, the serial number will be located on the processor. If it is not located on the processor, it will be located on the heatsink/fan unit. The diagrams below will help you locate your processor's serial number.
Identifying the serial number on AMD Athlon™ XP, AMD Athlon™ MP, and AMD Sempron™ Processors
Identifying the serial number on AMD Sempron™, AMD Athlon™ 64, AMD Athlon™ 64 FX, and AMD Opteron™ Processors