Liverpool score no goals against low level opposition despite shooting so much.
something something small club mentality

but seriously, you buy Dempesey and you might as well call it quits on trying to fit Carroll into the team. It's the whole Torres/Drogba/Lampard situation all over again (except even an injured, horrifically out of form Torres is still probably a better goalscorer than Carroll); no way he gets any kind of service, let alone the quality ones he needs to build his confidence and become a half decent striker.
still, since most people seem to be ready to give up on Carroll (I don't blame ya!) this could just as easily be a pretty decent stopgap for a cheap price. Not like Downing's crosses were connecting anyways...