If you have all of the other breakers turned off and the ONLY thing that is on is the Main breaker, then there is a problem between the main and the rest of the breakers, or between the meter and the main. If you have even 1kWH of power use when the Main breeaker is open, then that says there is a problem with the meter, socket or wiring after the meter. Given that the meter display is also non-functional, I'm going to go out on a limb and say it's a meter problem. If your main breaker is open, there is no way that there should be ANY power consumption whatsoever, not even 1kWh.
Another possibility however: Often times someone will tap into a neighbor's line, AFTER the meter, to siphon off power for things like grow lights for their pot plants. It's rare, but it happens because Law Enforcement can sometimes track down grow operations by monitoring power use so they steal power from neighbors to avoid detection. Look for evidence of a hidden extension cord or wiring that has been added when the house was abandoned. Thieves can be very clever in that respect. The drop to 1kWh may be the result of them seeing you looking at it so they curtailed their activity until you give up. In fact they may have damaged the meter display so that you could not see it running when all of your breakers were off.
