So here's the thing, some companies use a unique communication protocol between the charger and the device which means only their branded cable can hand shake with the headphones to initiate charging. It's an artificial restriction, tempers with open standards of USB but hey, that's how they milk more money …

Man, feel your pain! If it's still sticky after cleaning with alcohol, you might wanna try a DIY deep clean. Unplug your keyboard, pop out keys as much as you can with a keycap puller(not too harsh though), get a small brush and clean with isopropyl alcohol or warm water …