You've flashed both halves of the keyboard separately, you've then connected them with a TRRS cable, plugged your keyboard in to a USB port on your computer, and it turns on... but it won't send keystrokes? If that's the case, you'll likely have an issue with your USB cable.
To use your keyboard (and to flash it), you'll need to ensure your cable supports data transfer. Some cables only support charging and don't actually have the wires to transmit data, which is what your keyboard needs to talk to your computer.
A good way to ensure your cable supports data transfer is to use it to plug in your phone or tablet. If it then shows up on your computer as a drive, the cable will support data transfer and you can move on to the next step. Of course, you can also try other cables if you have them laying around. If you don't, purchasing a cable from a reputable brand like Belkin, Apple or Anker will usually be a good choice.
Once you've verified your cable does transfer data, you can move on to the next steps:
Seating the cables
Ensure the USB cable is seated fully into the USB port on both the computer and the keyboard. Do not use excessive force to plug the cable in, it should be firm but not forceful. Especially for Pro Micro controllers, using force may damage its USB port.
Ensure the TRRS cable is seated fully into the TRRS jacks on both the left and right side of the keyboard. Do not use excessive force to plug the cable in, it should be firm but not forceful. You can check visually that both cables are inserted equally deep.
If your keyboard still won't produce output, check whether the application you're typing in accepts keyboard input by using your previous keyboard to double check.
You might need additional drivers, for example if you're using an Elite C. You can check the troubleshooting step Unknown Device for DFU Bootloader for more information.
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