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
I looked at him—saw that a little more would make him dead-drunk—and all at once resolved on my plan.Mohun, or, The Last Days of Lee and his Paladins|John Esten Cooke
So they amused Alejo, gave him glass after glass of wine,—for he was a great drinker,—until finally he was dead-drunk.Filipino Popular Tales|Dean S. Fansler
Vow'd to revenge the dead-drunk peer Upon renowned St. Kitt.Tales and Legends of the English Lakes|Wilson Armistead
There is your Corporal there—le beau Victor—has been attacked by four drunken dogs of Arbicos, dead-drunk, and four against one.Under Two Flags|Ouida [Louise de la Ramee]
Huc says he never saw a Mongol unhorsed; but probably he never saw a dead-drunk lama forcibly put on a fiery steed.The Siberian Overland Route from Peking to Petersburg,|Alexander Michie