06:48 AM on 11/11/11
I'd have to say Hopesfall. they were so damn influential. although I don't know if you would categorize them specifically as "hardcore."
the easy answer would be Refused, At The Drive-in.
my other one aside from Hopesfall, a little-known Long Island band called Dearly Departed. God. I would stab a man to go back in time and see them play from the "Believing In Ghosts" era.