If the screen is not working or broken then you will have to replace the entire circuit board on the top part of the toy. The screen is soldered to the board directly by a ribbon. The device can be seen being taken apart in the main page of our device page.
If the buttons next to the screen are sticking together remove the front cover and then break them apart simply by bending them where connected. There are pictures and a guide on how to tear the device apart on our main page.
The first thing to do is to make sure both devices are powered on. After they are both on, push and hold the "Mode" button until both devices are connected. If they still don't connect, repeat until they do. (Wireless internet is not required for connection).