Hi. Do your brake lights work normally? When its not coming out of park the lights do come on, and now that it comes out without touching the brake the lights aren't stuck on are they?
Ok. If the brake lights work normally while the shifter is acting up that should rule out the brake lamp switch. That leaves two fairly common things.
It could be the blocker mechanism in the steering column. This is a link between the lock cylinder linkage that rotates and blocks the shifter from moving when the key is out. Its spring loaded, but they sometimes stick when you turn the key on and they stay in the block position and you can't move the shifter. This can be easily seen if you remove the steering column cover. You'll need a t-20 torx screwdriver to remove it. You'll see the piece I'm talking about, just make sure it moves with the key. If its sticking, have the dealer check to see if yours is covered under the recall. There was a recall for this blocker piece that covered alot of these columns.
The only other thing, and what I'm betting is your problem, is the shift cable itself. These do give some problems, and the fact that yours is coming out of park without touching the brake pretty much proves it bad. The brake/shifter interlock uses no seperate cable, it has a solenoid right on the shift cable. You can see it if you remove the knee blocker, the trim panel under the steering column. These solenoids act up and won't allow the shifter to move, especially when cold. Warming it up often helps. Sometimes you can still hear it click when you hit the brake, sometimes not. If your key cylinder linkage is ok and the brake lamps work normally, a shifter cable is pretty much a sure thing.
Sorry about the $ setback, but I'm glad I could help. Good luck!