I can't play any type of media or hear anything (with or without head/ear phones) on my iPod Touch 4th gen running on iOS 6.
I press play on the selected item but the play button immediately turns into a pause button.
You have a problem with the Audio chip on the iPod touch. iOS devices use a separate chip for decoding audio files, so that the processor can be put to sleep. The chip can probably decode all supported formats, but it may be optimised for mp3 and m4a. If the audio chip is dead, nothing will work. Movies won’t play because the iPod decodes only the video part (which has a dedicated chip on A5 and later devices) and not the audio.