Completely intoxicated, as in I can't remember a thing about last night; I was dead drunk. This phrase, first recorded in 1599, alludes to the immobility and insensibility of actual death.
Examples from the Web for dead drunk
But who was able to describe him, since the victim, you say, was dead-drunk at the time?Under Western Eyes
"Nor, he's dead-drunk," said Balla, picking up an empty flask.Two Little Confederates
Thomas Nelson Page
I am very angry to know that he is dead-drunk nearly half the day.The Correspondence of Madame, Princess Palatine, Mother of the Regent; of Marie-Adlade de Savoie, Duchesse de Bourgogne; and of Madame de Maintenon, in Relation to Saint-Cyr
Charlotte-Elisabeth, duchesse d Orlans; Marie Adelaide, of Savoy, Duchess of Burgundy; and Madame de Maintenon
They were the men told off to guard the tunnel; and they were dead-drunk.The Woman of Mystery
Such of the latter as were not dead-drunk were sleeping with men.What Shall We Do?