My brother's old old (CoreDuo) MacBook did the same thing for a while and eventually didn't charge at all, it ended up being something with the MB itself rather than the charger...which we didn't find ...
Following my good streak with Apple hardware, it seems my wife's early 2011 15" MBP has bitten the dust. White screens at boot, and blue screens during usage have hit me. I guess it's the dreaded GPU ...
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