Faulty headphones connector (no radio)

I have a problem with the headphones connector of my iPod.

The audio is perfect on both right and left headphones while the screen is on but as soon as I switch it off, there is no audio. I have looked for a solution and it seems that it is due to a bad connection in the headphones connector, something like if it is not completedly inside the plug. But it is.

When I try to use the radio, there is no radio available. The same problem, the headphones are "not connected" and there is no antenna.

Is there a way to solve it easily, without disassembling the iPod?