Well it not a serial # you want or need it's the service tag and or the Exprees service code. Both of these are on a sticker on the bottom of the notebook.
There is a model # other than what Dell calls it. My C610 has a model # of PP01L. And there is a Dell LBL P/N #.
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serail number dell laptop inspiron n5110 tag (Removed per TOU)