Recent hydrostatic simulations of solar active regions have shown that it is possible to reproduce both the total intensity and the general morphology of the high-temperature emission observed at soft X-ray wavelengths using static heating models. These static models, however, cannot account for the lower temperature emission. In addition, there is ample observational evidence that the solar corona is highly variable, indicating a significant role for dynamical processes in coronal heating. Because they are computationally demanding, full hydrodynamic simulations of solar active regions have not been considered previously. In this paper we make first application of an impulsive heating model to the simulation of an entire active region, AR 8156 observed on 1998 February 16. We model this region by coupling potential field extrapolations to full solutions of the time-dependent hydrodynamic loop equations. To make the problem more tractable we begin with a static heating model that reproduces the emission observed in four different Yohkoh Soft X-Ray Telescope (SXT) filters and consider impulsive heating scenarios that yield time-averaged SXT intensities that are consistent with the static case. We find that it is possible to reproduce the total observed soft X-ray emission in all of the SXT filters with a dynamical heating model, indicating that nanoflare heating is consistent with the observational properties of the high-temperature solar corona. At EUV wavelengths the simulated emission shows more coronal loops, but the agreement between the simulation and the observation is still not acceptable.