Cold brown dwarf atmospheres provide a good training ground for the analysis of atmospheres of temperate giant planets. WISEP J173835.52+273258.9 (WISE 1738) is an isolated cold brown dwarf and a Y0 spectral standard with a temperature between 350-400K, lying at the boundary of the T-Y transition. Although its atmosphere has been extensively studied in the near-infrared, its bulk physical parameters and atmospheric chemistry and dynamics are not well understood. Using a Mid-Infrared Instrument (MIRI) medium-resolution spectrum (5-18um), combined with near-infrared spectra (0.98-2.2um) from Hubble Space Telescope's (HST) Wide Field Camera 3 (WFC3) and Gemini Observatory's Near-Infrared Spectrograph (GNIRS), we aim to accurately characterize the atmospheric chemistry and bulk physical parameters of WISE 1738. We perform a combined atmospheric retrieval on the MIRI, GNIRS and WFC3 spectra using a machine learning algorithm called Neural Posterior Estimation (NPE) assuming a cloud-free model implemented using petitRADTRANS. We demonstrate how this combined retrieval approach ensures robust constraints on the abundances of major atmospheric species, the pressure-temperature (P-T) profile, bulk C/O and metallicity [M/H], along with bulk physical properties such as effective temperature, radius, surface gravity, mass and luminosity. We estimate 1D and 2D marginal posterior distributions for the constrained parameters and evaluate our results using several qualitative and quantitative Bayesian diagnostics, including Local Classifier 2-Sample Test (L-C2ST), coverage and posterior predictive checks. The combined atmospheric retrieval confirms previous constraints on H_2_O, CH_4_, NH_3_, and for the first time provides constraints on CO, CO_2_ and ^15^NH_3_. It also gives better constraints on the physical parameters and the P-T profile, while also revealing potential biases in characterizing objects using data from limited wavelength ranges. The retrievals further suggest the presence of disequilibrium chemistry, as evidenced by the constrained abundances of CO and CO_2_, which are otherwise expected to be depleted and hence not visible beyond the near-infrared wavelengths under equilibrium conditions. We estimate the physical parameters of the object as follows: an effective temperature of 402^+12^_-9_K, surface gravity (logg) of 4.43^+0.26^_-0.34_cm/s^2^, mass of 13^+11^_-7_M_{Jup}_, radius of 1.14^+0.03^_-0.03_R_{Jup}_, and a bolometric luminosity of -6.52^+0.05^_-0.04_logL/L_{sun}_. Based on these values, the evolutionary models suggest an age between 1 and 4Gyr, which is consistent with a high rotation rate of 6hr of the brown dwarf. We further obtain an upper bound on the ^15^NH_3_ abundance, enabling a 3-sigma lower bound calculation of the ^14^N/^15^N ratio = 275, unable to interpret the formation pathway as core collapse. Additionally, we calculate a C/O ratio of 1.35^+0.39^_-0.31_ and a metallicity of 0.34^+0.12^_-0.11_ without considering any oxygen sequestration effects.