I am not sure if the new key has the PATS stuff in it or not. I have called around and the dealership is by far the most costly. The want $100 and a local locksmith wants $35 per key.
When you identified your original key as the big key, you pretty much identified it as PATS. A PATS key has an RFID chip embeded in the handle. When you insert the key into the ignition the computer reads the chip and if it's ID matches one of up to six IDs stored in it's memory your computer will work with it. If the cut pattern of the key matches the cyclinder then you can rotate the ignition switch and all works. If the chip does not match one of the 6 stored IDs, or if the computer is unable to read the key's chip, your computer will not start the car even if the key rotates the ignition switch. So even if your new key does have a PATS chip, it is not paired with you car's computer so it will not work. If you keep trying to muck wih the ring, you may render the computer unable to read any key, then you are up the proverbial creek.
I know times are tough, but $35 is not bad for a new OEM key paired to your computer.
There are a couple of ways a locksmith can make a key for you:
DEFINITION: A "Master Key" is just a key whose ID has been paired (accepted and stored) into your car's computer.
1) Clone a master key: The key blank for these have an even fatter handle and do not have a FORD logo. After the locksmith cuts the teeth pattern, they read the ID from a "known working" key and write it to the newly cut key, hence you have a clone of the original key. In my experience these clones stop working in a couple of years. Also as far as your PATS system is concerned this cloned key does not count as a second master key.
2) Make a new master key: A new OEM blank is used, and it's chip already has an unchangable ID. The locksmith cuts the teeth and the key's ID is paired to your car's computer.
3) Pairing a new master: If you have two master keys (not a master and it's clone) you can pair it yourself. If you do not then the locksmith can connect a computer to your car and pair the new key in about 10 minutes.
I went through all of this on my Focus when the a cloned master died.
Good luck.