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Hello my name is***** do not rate until we are finished. I look forward to assisting and am very sorry to hear that you are having this problem.It is possible the keyboard itself has failed. But first Open Universal Access preferences (in System Preferences) and click the Mouse tab. Verify that Mouse Keys is Off. (With Mouse Keys on you can use the keyboard or the numeric keypad keys to move the mouse, however normal keyboard functionality will be disabled until the Mouse Keys feature is turned off.) If this did not work, please come back and let me know what happened when you tried it by clicking on reply to expert so we can continue. If it did work, please don’t forget to leave a positive rating - it is greatly appreciated.
It being brand new does not mean it works, it would just mean it could be defective. Can you try another or try this one on another Mac? That is the only way to rule it out since you already ruled out the ports themselves.
As I have told you twice before it is very likely the keyboard itself is defective (meaning a new device that does not work) and yes we have dealt with this before, normally it is caused by mouse keys. Since you refuse to accept that possibility I will opt out and open this to all experts rather than continue.
There is an easy way to find out if it is defective. First do this:
1. Shut down the computer.
2. Plug in the power adapter to a power source, connecting it to the Mac if its not already connected.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.
6. Press and hold the Command-Option-P-R keys before the gray screen appears.
7. Hold the keys down until the computer restarts.
8. Release the keys.
Then go to the Apple Logo to About this Mac then System Report. Select USB on the left if you see the keyboard listed on the right then the computer is seeing the device. Let me know.