Everything WAROSS said, plus - finding a phase a very low voltage to ground, possibly zero, is not unusual in ungrounded systems. In fact some systems have a phase deliberately grounded as normal operating conditions, but since that isn't your case, disregard it.
One grounded phase is a fault condition and should be treated as such, even though the equipment may operate normally for a long period. However, if it's an intermittent fault, it can create overvoltage spikes that will wreak havoc with your system, blowing out weakened insulation in a seemingly random fashion. Because of this, locating the cause of a grounded phase is a priority.
However, if the cause of the first grounded phase is not located, a ground on a second phase will be, in effect, a phase-to-phase fault with a path through your grounding system, and that opens up a whole different set of cases, the easiest of which is one of the faulted circuits tripping off due to overcurrent.
old field guy