The stock head unit also has a fuze in the back of the actual unit. At least mine does - model Cadence ZCD-6704A.
If you can measure 12 volts on both sides of the various fuzes, then the problem is obviously not there. Power to the plug will that goes into the head unit will confirm the wiring is OK.
Attached is a copy of the wire diagram from www.kiatechinfo.com
. There are actuallt three diagrams dependant upon the number of speakers/sub if you have it, but the diagram is essentially the same.
Hope this helps.