The clock works, but the radio does not

Answer is simple: The light works, the clock works, the stations show..but no sound so your radio is defective.
Two options: repair it if worth or replace it.

Depends on the radio.
General idea is this:
turn radio power off on face of radio. Clock should show.
push button such as SET / CLOCK / TIME
push other button HOUR MIN up down seek scan ff rew (one button will control hour other button will control minute)
turn radio power back on. clock should remain set.

the radio works
the clock works?
but the dimmer, park lamp in inside is burned out.?
turn the dimmer to make,
of all the other (many) park./dim lights are working then the bulbs are bad. the FSM shows all the steps for removing.
my guess, is you are asking why? above, but are you asking how?
i dont know.

scrap it

Either the fuse for the radio is blown, or the radio is dead. The clock is on a different circuit.

You have a defective part called a clock spring contact under the steering wheel, this contact is a coiled up simi rigid plastic ribbon with circuits embedded in it, after many years they l break and you loose the connection from the steering wheel controls (radio) and the Airbag. You must disarm the airbag on the steering wheel and remove it and replace the clock spring contact drum under the wheel, the cost is about $300.00

THE OWNERS MANUAL IN GLOVE COMPARTMENT WILL TELL YOU HOW TO TURN ON RADIO. RESET CLOCK ON RADIO AND TELL YOU HOW TO TURN ON AC + DEFROST AND HEATER.IT HAVE PICTURES SHOW YOU HOW THINGS WORK.

radio and clock dnt work on aveo fuses are gud keeps reseting clock radio is dead

The memory wire of the radio,(the power for the clock and channel settings) is usually connected to the same circuit as the cigarette lighter. (there is a seperate fuse for radio) Check your cigarette lighter socket for damage or dirt, etc. could be causing the memory fuse to blow. Also check your cig lighter accesories (like cell phone chargers,etc.)

P.S. The backlight is also a seperate circuit (connected to interior light/parking light circuit)

Try this, put the key in the ignition and let it be on the first turn right marked "ACC" or you can turn off the stereo and you will notice that only the Digital Clock screen will show. Turn the Volume/Audio/Sel knob and press on the "DISP" button simultaneously for about 4 seconds then release the "DISP" button. The digital clock will start blinking, and then use the Tune/Seek arrows pointing up and down to change the time. If the hour digit is blinking change the hour and after you have changed it press "DISP" then the minute digit will start to blink change it using the arrows, when you are done press "DISP" again or leave the clock for between 4 to 8 seconds the clock will start working normally.

I hope this works for you.

Good luck!

Aquinas