You've soldered the microcontroller onto your PCB, but the keyboard doesn't power on. You've tested the microcontroller and verified that it works, but when you plug the keyboard in, nothing happens. What now?
Test each side individually
Don't connect both halves with a TRRS cable at first, and connect a half directly to your computer with a USB cable. Do they work individually, but not when connected together? Then you should read Only one half of my keyboard works at a time, but not when they are both connected.
Test both halves at once
Next up, connect both halves with a TRRS cable, and then connect one of those halves to the computer with a USB cable. The keyboard should now work as you'd expect (though if you're here, it likely won't, yet).
If it doesn't work, unplug the keyboard from your computer, and unplug the TRRS cable. Look at the rings on the TRRS cable and count: does it have four contacts, separated by colored or black rings? Chances are your cable is actually a TRS cable, in which case it only has three contacts.
If you happen to have a second TRRS cable, retry the test with that, sometimes the cable might be broken.
Next up, you'll want to make sure the solder joints on your TRRS jacks and microcontroller are good. Adafruit has an excellent overview of common soldering problems. Compare your solder joints with those in the guide, and if any have problems, rework them to match with the correct examples in the guide.