Why won't my cousin eat anything?

My cousin refuses to eat anything but chicken nuggets, cheese sticks, hot dogs (no bun), and ice cream. When he was younger I wasn't too worried about it, but now he is almost 14 and the problem hasn't gotten any better. We have tried to be firm with him, but nothing seems to work. Once during lunch we said that he couldn't leave the table until he ate some corn. He didn't move until it was time for bed and we gave up. I am very concerned and don't want to see him eating like this when he's an adult. Does anyone know some method to coax him into trying new foods? Please help.