Even though you did not set the Alarm, did you check if the 'circular' turner is set to OFF. Sometimes, I had accidentally touched the circular turner to set it to radio and the radio would come ON automatically.
The radio and the alarm are separate. You can set the clock to AM or FM on the side and tune in to the station of your choice. On top of the clock are two buttons marked radio for on and off. Press the on button for the radio, and off button to turn it off.
To set the alarm mode, toggle the switch to radio or buzzer and set the alarm time. I like the buzzer. It has a nice quiet beep that gets increasingly insistant as time passes before you turn it off. Don't forget to turn the toggle to off if you don't want to wake up. :-)
Make sure the circular button on the left is turn to "off". The small dot on the wheel should align with the black dot just above "alarm mode" that says OFF. Then be sure you have pushed the OFF button on the right. Hope this works!