Since the secondary side of a transformer is a new service there must be a grounded conductor. Since there is no XO from the primary the secondary must be corner grounded. In other words one of the secondary phases (it doesn't matter which one but H3 is cutomary) must be bonded to the EGC. This phase will then read 0 volts to ground while the others will read 277 volts and voltage phase to phase will be 480. When this is not done properly the problems you have described will frquently occur. Usually the whole thing will fail to function at all, but I have seen what you are describing happen, in exactly that way.
If you have never done this, it seems counter intuitive and it makes you cringe when you turn it on.( I know I did the first time) Also the grounded phase must be color coded gray or white.