Fallen cold and dead.
2
O Captain! my Captain! rise up and hear the bells;
Rise up—for you the flag is flung—for you the bugle trills;
For you bouquets and ribbon'd wreaths—for you the shores a-crowding;
For you they call, the swaying mass, their eager faces turning;
Here Captain! dear father!
 This arm beneath your head;
It is some dream that on the deck
You've fallen cold and dead.
3
My Captain does not answer, his lips are pale and still;
My father does not feel my arm, he has no pulse nor will;
The ship is anchor'd safe and sound, its voyage closed and done;
From fearful trip, the victor ship, comes in with object won;
Exult, O shores, and ring, O bells!
The speaker continues to refer to the Captain as a  father figure.  The Captain’s head rests against the speaker’s arm, but he can’t feel anything because he has died. His lack of “pulse” and “will” may suggest the political willpower that is dying with him. 
 The speaker’s failure to revive the Captain contrasts with section 40 of  “Song of Myself,”  in which Whitman portrays himself as an almost Christ-like healer of the dying: 
 
 I seize the descending man and raise him with resistless will, O despairer, here is my neck, By God, you shall not go down! hang your whole weight upon me. 
 [….] 
 Not doubt—not decease shall dare to lay finger upon you; I have embraced you, and henceforth possess you to myself; And when you rise in the morning you will find what I tell you is so. 
 
 “Song of Myself” appeared in 1855; Whitman went on to  volunteer as a nurse during the Civil War.  His experiences in army hospitals may have sobered his vision of himself as healer, while influencing lines like this one.
O Captain My Captain