I'm going to assume here that when "pushing the brakes a few times" you're not deactivating the emergency brake, and that you've had the good sense to do that already before trying to move.....

That said, it sounds like your brakes are sticking, or the drive selector is misbehaving.

Do you have to press the brake pedal to change from Park to R/D/N? If not, I suspect the brakes. In that case, do you hear any grinding/squealing or feel any rubbing/grinding? If so, get a brake inspection done at a shop, but I don't suggest driving it there, as you'll only do more damage than good.

If you do have to press the brakes to shift into a gear, make sure you are depressing the pedal before moving the shifter at all, and ensure the shifter is fully in position prior to trying to go anywhere. If this careful, full shifting works, and you can live with it, great. If you can't live with it, go to a repair facility or dealership to get it fixed (you're likely looking at steering column disassembly or transmission work).

Also, refrain from trying to change to opposing gears while the vehicle is in motion (putting it in D before you've stopping rolling out of a stall, etc), because this forces the engine, transmission, and drivetrain to rapidly and violently stop a ton of torque and start the mass moving in the opposite direction. Lucky you, you won't feel much of a **** because of all the vibration dampeners built into modern vehicles, but trust me, the vehicle feels it.

Keep in mind, it's always worth asking a local repair facility or dealership for a complete list of TSB's (Technical Service Bulletins) and Recalls, to look through them for weird issues. Remember, dealerships will only send you a letter/notice if it's a safety recall, the rest of it they consider YOUR resonsibility. Who knows? It may be a faulty shift selector that the manufacturer has an update for because of this issue.

Hope this helped.