... and plug it directly into the back of the ESX ...
you may use the DCUI to find out the correct port(s). However, a direct connection may be tricky, especially if the ESXi host's Management network uses VLAN tagging, and if it has more that one vmnic. Anyway, assuming that the physical network (switches, routers, etc.) are up, and working correctly, and if the ESXi host can reach/ping its default gateway, you should be able connect to it over the network.
Another option is to enable ESXi shell access and power on the important systems (e.g. your DC/DNS/DHCP server) from the command line.
André