The contacts for the left and down cursor may be dirty. Being an un-used device they shouldn't be worn out.
Here is a link to the ifixit repair guide for the device.
Here is an image taken from the repair guide. I have highlighted which contacts need to be cleaned, both on the board and on the rubber pad. (The rubber pad contacts have a conductive coating which bridges across the contacts on the board, when the button is pressed down completing the electrical circuit)
Use a Q-Tip moistened with IPA 90%+ (Isopropyl Alcohol - available at most pharmacies - do not use 'rubbing alcohol' as it is not as effective)
(click on image to enlarge for better viewing)
Take note of the caution issued at Step 9 in the ifixit teardown instructions
Alternatively since you stated that you bought an un-used device, did it come with a warranty at all?
If so follow up on getting a warranty repair or replacement as by trying to fix it yourself as shown above, will void any warranty.
Hopefully this is of some help.
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