first question is whether or not the S meter in the radio is showing it receiving signals or not.
if it is, then it sounds like a bad audio chip. there are more possibilities than that, but IC chips do go bad.
a quick test you can do is to turn the volume on the radio all the way up, and touch your finger to pin 4 of the audio chip. (IC 8 located on the right side of the radio with the component side up and the knobs facing you)
http://www.cbtricks.com/radios/galaxy/dx959_mosfet/graphics/dx959_mosfet_sch.pdf
if the audio chip is still good, you should get a hum from the speaker with your finger on pin 4. (pin 1 is closest to the front of the radio, and yes, your finger will be too big to just touch pin 4. dont worry about touching the other pins)
if you dont get the hum then the next step is to measure the voltages on each pin of the audio IC. checking them against the service manual found here:
http://www.cbtricks.com/radios/galaxy/dx959/graphics/dx959_serv_manual.pdf
if the voltages you measure are significantly different than the voltages that the service manual shows, then you can be pretty sure the audio chip is bad and just replace it.
be sure to read up on the proper way to replace a chip like this.
heat sink compound, isolated from the chassis and such.
good luck,
LC