HT1529: Mac OS X: About This Mac window provides computer serial numberLearn about Mac OS X: About This Mac window provides computer serial number
Currently Being ModeratedJun 12, 2013 3:57 PM (in response to vinayakvaidya)
Try resetting your computer's system management controller (SMC) to see if that helps (see here for how to do this: http://support.apple.com/kb/HT3964).
Beyond that, you can try using another power supply, in the event the problem is a broken power adapter.
Lastly, if neither of these show differences, then you will need to take the system in for servicing, as there may be a damaged component on your system's motherboard or other power-handling circuits.