Being a musician I've had a lot of issues with 1/4" cables. They take quite a beating over time and tend to quit on you. Most times I am able to open them up and find that the joints at the wire-plug connection have broken. It's very easy to fix them and can save you some money if this is a regular occurrence.
Most times the plug of the end will have a screw-off sleeve.
First twist this open. Slide back and protective sleeve that might be under that and take a look at the connections.
There should be two leads coming from the wire, one wrapped around the other, each soldered to their own spot on the jack.
The cable here is a coaxial cable. It uses an outer conductor as ground to shield the internal conductor carrying the signal.
The way the cable should be connected is that the outer conductor should be soldered to the longer terminal (the more outer one) that clamps to the cable and the inner conductor should be connected to the shorter terminal.
You may need to remove the cable from the jack completely (carefully pry the clamp part open with pliers) and re-strip and solder the cable. Be careful when stripping the cable, it can be difficult at times. Strip the outer layer of rubber, then carefully pull the webbed conductor apart and around to one side. Then strip away the inner rubber layer and twist the inner conductors together. I was trying to get this one done quickly and i accidentally took the outer conductor off too. It should be between the white coating and the black outer coating..
Then replace it on the jack, solder the two joints, and screw the sleeve back on. Remember the sleeve must be ON THE WIRE before you solder the end of the jack on. Double check this first, otherwise you have to pull the jack completely back off. It's easiest to just leave the sleeve on the wire in the first place.