We present the results from our 7yr long broadband X-ray observing campaign of SN 2014C with Chandra and NuSTAR. These coordinated observations represent the first look at the evolution of a young extragalactic SN in the 0.3-80keV energy range in the years after core collapse. We find that the spectroscopic metamorphosis of SN 2014C from an ordinary type Ib SN into an interacting SN with copious hydrogen emission is accompanied by luminous X-rays reaching Lx~5.6x10^40^erg/s (0.3-100keV) at ~1000 days post-explosion and declining as Lx{propto}t^-1^ afterwards. The broadband X-ray spectrum is of thermal origin and shows clear evidence for cooling after peak, with T(t)~20keV(t/t_pk_)^-0.5^. Soft X-rays of sub-keV energy suffer from large photoelectric absorption originating from the local SN environment with NH_int_(t)~3x10^22^(t/400days)^-1.4^cm^-2^. We interpret these findings as the result of the interaction of the SN shock with a dense (n~10^5^-10^6^cm^-3^), H-rich disk-like circumstellar medium (CSM) with inner radius ~2x10^16^cm and extending to ~10^17^cm. Based on the declining NH_int_(t) and X-ray luminosity evolution, we infer a CSM mass of ~(1.2f-2.0f^0.5^)M_{sun}_, where f is the volume filling factor. We place SN 2014C in the context of 121 core-collapse SNe with evidence for strong shock interaction with a thick circumstellar medium. Finally, we highlight the challenges that the current mass-loss theories (including wave-driven mass loss, binary interaction, and line-driven winds) face when interpreting the wide dynamic ranges of CSM parameters inferred from observations.