The top plastic part of the headband on my headphones cracked. I tried to fix it with superglue, but that did not fix the...

It depends on what problem you are having with the audio cable. You can check the following troubleshooting guide (Troubleshooting Beats Studio First Generation) to help diagnose the problem. If all else fails, the guide recommended by oldturkey03 should be great for soldering on new jacks. If the in-line buttons are the problem, it would probably be easier to buy a new cable.

Oscar, another possible solution is replacing the batteries. Unlike some headphones, Beats Studios will not work without batteries. You can access the battery housing by twisting the circular piece of plastic with the Beats logo that is on the side of the headphones with the audio cable jack. The plastic cover should turn a little and then fall off easily. This guide walks you through what I just explained: Beats Studio First Generation Batteries Replacement. Hope that helps! If the replacing the batteries does not fix the problem, I would recommend looking through this troubleshooting page: Troubleshooting Beats Studio First Generation