It is clear that galaxies in local clusters are different from those in the field. Environment must play an important role in shaping the ensemble of galaxies. However, we do not yet know when these physical processes are initiated and what mechanisms directly impact how galaxies evolve. We are using the Australian Telescope Compact Array (ATCA) to study the role of environment on the molecular gas content, the fuel of star formation, of distant star-forming galaxies. These are the likely progenitors of elliptical galaxies which dominate the light in local galaxy clusters. From our pilot survey to search for low-surface brightness cold CO(1-0) molecular gas emission, I present the discovery of massive extended CO gas reservoirs in these star-forming galaxies that are located in the galaxy cluster in formation surrounding the radio galaxy, MRC1138-262, the so-called Spiderweb protocluster, at z=2.2. The discovery is unexpected as gas truncation and stripping was predicted. Our results alter our view of the important topics of the development and gas phase distribution of the "proto-intracluster medium": how ram pressure stripping may operate in galaxy protoclusters, how the galaxies may contribute to enriching and heating the proto-intracluster medium, and how their star formation may be limited by their internal dynamics. Furthermore, I will present results of our on-going ATCA Large Program, CO ATCA Legacy Archive of Star-Forming Galaxies (COALAS), based on our successful pilot survey. Our sample consists of well-covered 'field'-targets from the ALMA survey ALESS in the ECDFS and protocluster galaxies surrounding the Spiderweb. This survey significantly extends our study of how environment impact the cold molecular gas content, gas excitation and star-formation efficiency in cluster and field galaxies in the early universe. Currently, the ATCA is the only interferometer in the southern hemisphere that can target at high redshift the ground-transition CO(1-0), the most robust tracer of the overall cold molecular gas mass and distribution. Thus the ATCA is a crucial complement to ALMA. Our ATCA data are complemented by exquisite multi-wavelength data from the ESO telescopes and ALMA, thus demonstrating the strong synergy between facilities from ESO and Australia and the close collaboration between both communities.