I had the same problem! My model is iDL43 and it is only 2 months old. I just fixed the problem!! I called the iHome Audio people (I-800-288-2792) - You may want to call because there may be different instructions for different models but this is what they told me to do:
1. Unplug clock/radio
2. Take batteries out of bottom of radio (unscrew and remove batteries, you may not have realized there were batteries!)
3. Wait 20-25 minutes for clock/radio to 'reset'
4. Plug clock/radio back in
5. Viola!! IT WORKS!
6. The woman at iHome Audio said if it works then you can put batteries back in, if it doesn't work call them back. I am not putting the same batteries in, they are an unknown brand, maybe old(?) or cheap.