Check whether your phone requires to connect a headset for listening to radio stations. If the radio is turned on and no messages on the screen of the phone was detected, but no sound, then find in settings the option "Play through the external speaker".
If the radio on your phone refuses to run without a headset, you can use part of the old headphone. This requires scissors to cut off the cord, leaving 5-6 cm from the plug (Jack).
Even if the focus is with broken headphones did not help, there is always the option to install a third party app and listen radio through it. The only drawback of this method is that usually such software requires a connection to the Internet and therefore charge web traffic.