Ok, little update here.
I talked to the NJ dealership, SOA, and my local PA dealership this morning. All regarding the no inspection issue. End result is that I have to pay for inspection on my brand new car. The NJ dealership says they didn't do it because I'm registering the car in PA, so they literally couldn't. Makes sense. I called SOA to see if they could set me up to go to a PA dealership and get this done. The guy was friendly and all, and talked to my local dealer, who I then called. They said they would treat it like any other inspection, full cost.
Not sure what I expected, as each dealership is separate from each other, but I was hoping for some kind of cheaper solution to this. Oh well, I guess I'll chalk it up to New Car First Time Buyer Gaffs. It's probably something I should've addressed with the dealership before I bought the car, but I didn't really think of it.
I would be interested to hear from anyone else who may have bought in another state, though. And maybe I should put an informative post in the Order thread in New Members. Or is this something that is general knowledge that I was out of the loop on?