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We present NuSTAR hard X-ray observations of Sh 2-104, a compact HII region containing several young massive stellar clusters (YMSCs). We have detected distinct hard X-ray sources coincident with localized VERITAS TeV emission recently resolved from the giant gamma-ray complex MGRO J2019+37 in the Cygnus region. Faint, diffuse X-ray emission coincident with the eastern YMSC in Sh2-104 is likely the result of colliding winds of component stars. Just outside the radio shell of Sh 2-104 lies 3XMM J201744.7+365045 and a nearby nebula NuSTAR J201744.3+364812, whose properties are most consistent with extragalactic objects. The combined XMM-Newton and NuSTAR spectrum of 3XMM J201744.7+365045 is well-fit to an absorbed power-law model with NH = (3.1 +/- 1.0)E22 cm^-2 and photon index Gamma = 2.1 +/- 0.1. Based on possible long-term flux variation and the lack of detected pulsations (< 43% modulation), this object is likely a background AGN rather than a Galactic pulsar. The spectrum of the NuSTAR nebula shows evidence of an emission line at E = 5.6 keV suggesting an optically obscured galaxy cluster at z = 0.19 +/- 0.02 (d = 800 Mpc) and Lx = 1.2E44 erg/s. Follow-up Chandra observations of Sh 2-104 will help identify the nature of the X-ray sources and their relation to MGRO J2019+37. We also show that the putative VERITAS gamma-ray excess south of Sh 2-104 is most likely associated with the newly discovered Fermi pulsar PSR J2017+3625 and not the HII region.