Hello,
First, check the antenna for your i-pod, make sure it is having reception because if there is no reception, the radio won't work. Also, make sure it is on FM frequency.
If non of the above is the cause of the problem, then it means the turner of your radio is defective or the antenna may have be disconnected from the inside of the i-pod.
Get a screw driver, use it to carefully disassemble the i-pod, first, make sure the antenna is intact, before checking on the turner.
Check the below picture to have an idea of what the turner looks like;
The turner is the black long thing at the left side of the board. It usually have a coil round about it. I don't means this is the board of your i-pod, but it must have a turner.
If you don't find any obvious fault on the turner, then I would suggest you take the i-pod to a repairman to fix the fault for you.
Good luck.