We report the radial-velocity discovery of a second planetary mass companion to the K0 V star HD 37605, which was already known to host an eccentric, P~55 days Jovian planet, HD 37605b. This second planet, HD 37605c, has a period of ~7.5 years with a low eccentricity and an Msini of ~3.4 MJup. Our discovery was made with the nearly 8 years of radial velocity follow-up at the Hobby-Eberly Telescope and Keck Observatory, including observations made as part of the Transit Ephemeris Refinement and Monitoring Survey (TERMS) effort to provide precise ephemerides to long-period planets for transit follow-up. With a total of 137 radial velocity observations covering almost eight years, we provide a good orbital solution of the HD 37605 system, and a precise transit ephemeris for HD 37605b. Our dynamic analysis reveals very minimal planet-planet interaction and an insignificant transit time variation. Using the predicted ephemeris, we performed a transit search for HD 37605b with the photometric data taken by the T12 0.8-m Automatic Photoelectric Telescope (APT) and the Microvariability and Oscillations of Stars (MOST) satellite. Though the APT photometry did not capture the transit window, it characterized the stellar activity of HD 37605, which is consistent of it being an old, inactive star, with a tentative rotation period of 57.67 days. The MOST photometry enabled us to report a dispositive null detection of a non-grazing transit for this planet. Within the predicted transit window, we exclude an edge-on predicted depth of 1.9% at >>10sigma, and exclude any transit with an impact parameter b>0.951 at greater than 5sigma. We present the BOOTTRAN package for calculating Keplerian orbital parameter uncertainties via bootstrapping. We found consistency between our orbital parameters calculated by the RVLIN package and error bars by BOOTTRAN with those produced by a Bayesian analysis using MCMC.