Try testing the dash cam using the supplied 12v Car power cable with the 12v socket in a vehicle. If this works correctly then there may be a problem with the installation of the Hardwire Kit. Please ensure that the Hardwire Kit has been earthed correctly to an unpainted part of the vehicle chassis, try a new earth position if you still receive no power.
Connect the hardwire kit directly to the battery terminals to see if there is anything wrong with the cable.