Make him an assassin, on the run from the cops and the Bat for murder. Tries to kill himself rather than get taken away. Fails. Realizes while in prison that he's immortal. From there, he could escape to try to prove his destiny wrong (i.e. - try to die). Perhaps when he escapes, he kills out of wishful thinking, bitterly envying every life he takes. I think that'd be a great, fresh way of approaching that character...
