If the system is completely ungrounded it can float to anything it feels like. So some part of the system will couple to ground - for DC by leakage, for AC by leakage and/or capacitance - and the rest of the circuitry will be at some voltage with respect to that defined by the voltage difference between different parts of the circuitry.
Danger, danger, danger.
Even capacitive coupling can drive lethal currents through wet skin resistance. It only takes something like 20 ma up your left arm to do you in. If you can feel a shock when touching things the situation is dangerous.
You should drive a good ground rod then pick some part of the circuitry and ground it. (Probably the negative side of the battery. Also, if you are running an inverter and it's a model isolates the AC you'll need a ground on that side, too.)
An alternative to a ground rod is a foundation grounding system. If you bought the house or had it constructed to a purchased design (rather than building it yourself) there may already be one in place. Look for a wire emerging near a likely site for a utility feed if you don't have the plans and can't contact the builder.
ONE ground rod. ONE point gets grounded by ONE path. (Otherwise you're creating a greater lightning/surge current risk and potential for working current to travel along protective ground wires and start a fire.) If you have any metal plumbing it should be tied to the ground at ONE point (plus a bypass from cold to hot at the water heater unless copper hot and cold pipes are soldered together somewhere). Metal gas pipes should also be tied to either the electrical or water pipes in ONE place.
Once you have your grounding system set up, measure the voltage (both AC and DC) from the point you intend to ground to the grounding system. Then measure the current from ground to the grounding point - directly with a meter if the measured voltage was low, with a lamp in series with the meter if it was high.
If you get more than a few milliamps AC or DC (or light the lamp), hunt down and fix the leak before making a permanent connection.