Pretty common problem: dirty or misaligned switch contacts on the jack. Normally, without the headphones plugged in, the jack's contacts close the circuit to the audio amp that feeds the speaker. Inserting the headphone plug opens that circuit and sends the lower-level signal to the cans (headphones). Open the radio up (unplugged, of course) and check out the operation of the phone jack. You'll be able to see the action of the switch opening and closing -- or trying to. If it's bent, you might find a "closed-circuit 1/4 inch phone jack" and just replace the old one.