What do a serious look and a dishpan have in common?
Plenty. The word "pan" has been used since the 19th century to mean "the face," possibly because the human face is broad and shallow like a dishpan. Add the word "dead," and a deadpan look would be one that's so broadly unanimated as to have not even a twinkle of expression.
In the past few hundred years, however, this common word for a "poker face" (the card game, not the fireplace tool) has moved beyond the visage. A deadpan news story is similarly lifeless - and don't expect any humor or feeling in someone's deadpan remarks.
SOURCES: 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; Webster's Dictionary; The World Book Dictionary; 'The Random House Dictionary of the English Language.'