I thought these 4.6 engines will not start with out the proper key..Isnt there a theft light or something on your dash? I allways thought the keys were chipped and when inserted in the ignition this sends a "GO" to the PCM for start up? What is this theft light for then?
Anyway....Man you are one lucky SOB....I have a friend that posted his 5.0 on CL and the next day was gone...R.I.P.......
He let the entire world know that under his hood he was 10 grand invested. The only thing he had left was an old leak spot in the driveway and the add on CL. So yea....You made out..!!!!!

If I was you (wich I couldnt even begin to imagine), I would change my oil and maybe flush the gas tank. I might just be crazy paranoid but if they blew your tires, they could of been like "Lets F.. this car up" and pour crap in the engine and gas cap.
Im not trying to make your situation worse bud...Just saying what Id do.

Oh yea, Id wash that thing from top too bottom and check for illegal chit...(under the seats, trunk. ect..)
GOOD LUCK!!!!!!!