My guess would be that the fob is knackered, the transponder is glued into the the top of the key part so you could split the key and the remote to check if it's the transponder.
Mine failed last year at 10 years old, the light still came on when I pressed either button, but wouldn't communicate with the car. I had a spare remote from when I was going to swap to a flip key and just added that using VCDS.