Well, typically I have venomous shipped DASH to La Guardia without any trouble, so monitors shouldn't be a problem. They check ID...but just to verify you're the recipient. As for Newark, check on NJ's laws for monitors. I actually have to ship from Newark b/c I am not Delta verified, so I ship NW Air Cargo. Unfortunately after 9/11 they closed their terminal at LGA and only accept incoming at Kennedy.
TO ship venomous from Newark, I received a Letter of Authorization to transport venomous snakes/heloderms/crocs to EWR solely for shipping purposes....otherwise, they as you know, are illegal in NJ.