"New" key, Car Won't Start

When I purchased my car used, it only came with 1 key, so I picked up a few items after reading some threads here to have two keys, and I've run into a little bit of a snag.

I bought this: From Ebay. It has the same FCC ID as mine and I was able to program the car to it so that the doors unlock and lock and the trunk opens. It was a used key so the next thing I needed was one of those flip key shells with a blank to be cut to match my existing key.
I bought this one: From Ebay.

I had it cut and the fits in my doors and unlocks and locks them and turns the ignition from lock to accessory to on and to start. When I try to start the car, it turns over once or twice and then stops and doesn't start.

My guess at this point is that this is a PATS system, but what do I need to do so that my car recognizes the key and starts?

Ok, I think I've answered my own question. I read further forward in the manual (before programming the transmitter section) about the immobilizer. Apparently I'm going to have to take these keys into a dealership and get the immobilizers programmed to have this corrected.

$$$

Transponder keys are big money to the stealerships. Whether by design or by accident, we got a single key at signing when I bought my legacy, and another key and valet key in the mail almost a month later. I was so freaking happy to get that second and third key since I was already wrestling with the idea of buying one.