With a bad cable you'd still hear the actuator firing, it just wouldn't open the fuel door. With my bug the door opened but never closed again until I replaced the cable. My bad cable was still able to release it just couldn't reset to close the door.The fuse to check is #38, should be 15 amps. Here is a DIY on the fuel door cable:
The actuator is under the rear trim on the right side. You could remove it and test it with a 12 volt battery. The cables are a very common problem. They tend to get kinked and then won't release the fuel flap.