You MAY have gotten one with a dead battery, the unit is several years old and currently discontinued. First thing to check is the switches. Make sure the radio volume knob is OFF as it can drain the battery even when you can't hear the music. Same with the light (the round switch on the top above the lens).
Then check the band selector switch. It may be on one of the Weather frequency settings, which will also use power.
If you switch off all the other features that can drain power and you STILL can't charge the internal rechargeable battery, open the battery compartment up with a small screwdriver. Check if the battery is connected, it has a small plastic connector that snaps on and off. It may be not seated firmly enough to complete the circuit so the generator can charge the battery. Rechargeable batteries eventually need to be replaced, and you should be able to read the voltage and model of the battery so you can purchase a replacement here on amazon or from Radio Shack.
That should fix it, but i suppose there could be a problem with the generator itself. If the handle isn't tightly holding the axle of the generator, it won't supply enough rpm's to generate enough electricity. Inside, the wires from the generator could have been damaged if the unit was dropped.
Experiment with different things that could be wrong. Instead of trying to charge it with the hand crank, try putting it in a sunny window for a few hours, then try the light or radio. If that solves the problem, it may be the generator that is faulty, and amazon SHOULD replace it for you. If nothing gives it a charge, try getting a replacement battery from radio shack or amazon. It's very easy to replace, depending on how diy you are.
It really is a great radio, and there must be a distinct problem (or oversight) with yours causing it to malfunction. You shouldn't be having all these problems, mine work flawlessly (i have 2).
But try experimenting with a few of the suggestions i made, if it still doesn't work, call amazon customer service 866-216-1072 and tell them they need to replace the defective item. Let me know how it works, either way, i'm pretty puzzled by this.