You need to establish whether you have onboard sound (i.e. integrated) or a sound card.
If you have a sound card you should find out the make and model and download the latest drivers for it; in the case of the onboard sound, you will need to ascertain if it is provided by Realtek, C-Media or possibly SiS and, again, download the latest drivers.
You are correct in that the round green jackplug on the rear of the onboard/sound card is the output for the speakers.
How, by the way, are you trying to listen to a radio station? Is it via the Internet or a Freewview TV card or USB stick?