Does the car unlock when you pull the drivers' door handle? If so, that means the KG antenna on the left side of the car is working properly (a good thing!), and simplifies things greatly. I'm assuming you don't have access to an SDS. If you do, diagnosing KG issues is a breeze.

It sounds like the push contact may have failed. Does the button feel "soft" when you push it, compared to the button on the passengers' side? This is a pretty common problem on KG cars. If the button feels the same as the other one you might want to make sure it's connected properly. I've had several cars where I've found the wires disconnected or damaged (bodyshops, boneheads, etc.). You'll need to remove the inner door panel to do this. The push contact is part of the exterior handle, and the wires come out of the handle on the opposite side of the button. If eveything checks out, replacing the handle will probably solve the problem.