Electric kettles are (electrically) incredibly simple. I don't doubt you have the skills to repair one. However, in practice I doubt it is a good idea for a couple of reasons. First, they are designed as disposable consumer electronics. It will likely be quite difficult to disassemble, find the fault, fix it, and reassemble. Second, these kettles have a fairly high power density. Despite the simplicity, a botched job is a serious fire hazard, and it isn't necessarily clear what the penny pinching manufacturers are relying on for thermal safety.
My suggestion is to try to take it apart and diagnose the fault. Repair it if possible, but after carefully testing it, chuck it and buy a new one. If you don't have the willpower to throw out an apparently working kettle, then I say don't attempt the repair.