Program key?

Can you clarify some things for me?

1. When you push the buttons on the key fob, it does not lock or unlock the car, is that correct?
2. Have you checked the battery in the key fob, when you push lock or unlock, does a red light flash next to the lock button on the key fob?
3. Does it have the little black buttons on the driver side, passenger side, and hatchback door handle?

 

is the button under the steering wheel in the correct position?

 

The correct position is 'OUT' but the button under the steering wheel only affects the operation of the SKS (keyless) lock/unlock. It doesn't affect the fob buttons (remote) lock/unlock.

I suspect the previous owner replaced the key fob with a secondhand one which can only program the RFID chip to allow the car to start with the fob in the slot. The remote and SKS features can be programmed with a used key fob.

To get the SKS working the OP will need to purchase a brand new virgin fob and do an 'all keys' lost procedure which will involve getting a 'seed' code if they want to do the procedure themselves or a visit to a dealer or an authorized locksmith to have it done for them. In short, this will be expensive to really expensive depending on which option the OP chooses.