Yes the keys do have chips built into them.My versa does not have a key fob per say because i dont have power locks. But what i have noticed is the factory keys have some sort of chip or similar in them. I had the key copied at home depot near me the copy can unlock the door and trunk and even turn the ignition into any position, however the copy will not start the car it wont even make the starter engage. Knowing that it seems like your issue might be with the key fob itself. My fob does not have any way to open it to replace a battery or anything like that i would check yours to see if there is a replaceable battery and try that first.
And the remote (for the doors) can be opened up to change the battery. There is a how to video on you tube for that.