Unfortunately when it drips like that instead of spraying it does indicate a damaged head. I've never seen a brand new one do that though. Usually the damage is caused by flushing the head too hard or the head is very old and just worn out. Did you flush the head before installing it? That's a step we normally advise against even though it's in the service manual because it seems to cause more problems than it solves. I for one have put in 100's of heads and never flush. If you did flush, there is a possibility that you pushed too hard and that caused the issue.
If you really want to be sure before getting a new head, do a damper swap. Simply swap the positions of the black damper with the one next to it but keep the ink lines attached. Run a cleaning and then a nozzle check. If the black can print in a different channel, the head is probably fried. If the black still doesn't print in the new channel and the other colors can print though where the black was, it's more likely an ink flow issu