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Make sure the brake lights work 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, try an lubricate it and get it working again.
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.
The brake lamp switch is located on the pedal bracket just above the brake pedal. If you look up there you won't be able to miss it. Its easy to replace, just unplug it and turn it and it comes out. when you put the new one in you have to move the adjustment lever over to adjust it, its the little red lever.
If it was the brake/shifter interlock solenoid you were asking about, its part of the shift cable. You have to get a shift cable to replace the solenoid, its all one piece. The cable isn't hard to replace either. the brake switch you may be able to get aftermarket, I doubt you'll be able to find the shift cable anywhere but a dealer though. Either way, niether of these parts are expensive at a dealer, and will likely be in stock.