There were no disasters; I've long had another alarm clock set to beep at me a little while after the radio was set, so that's been waking me. But it took away the extra layer of security!
Yesterday I stopped at Radio Shack (the new store next to Gallager's, on the corner of Fulton and Meadow Streets, a reincarnation of the Triphammer Mall location) to get a new pocket radio since I haven't been able to find mine, and I needed one for election night. They also had several clock radios, including one marked "Clearance - $24.97."
It's an RCA with digital tuning, the ability to let me fall asleep on one station and wake up on another, a gradual wake that starts the radio quietly and then slowly makes it louder, and even a battery backup if I plop a 9-volt battery in. Nice, tall, green numbers.