Since you're seeing some kind of power applied to the LEDs for a second, my guess is:
90% Chance you have a bad shorted USB Mini-B connector on the keyboard side. It's an SMD connector part on a small module on the underside of the board. I doubt CM will send you a new module so your best bet is finding someone who spilled something on their board and is selling it for cheap, then salvaging the module/connector. However, if you're persistent in your web searching then you may be able to find the same connector for sale and replace it yourself granted you can solder SMD components with some finesse.
10% Chance you have a bad controller or more complicated issue; i.e. xtal/resonator, uProc, etc. Costar does have a minor history of controllers just up and dying (I've a couple boxes of dead FILCOs lying around.), but it's still much more unlikely than a connector issue.