There are 2 outer wires, the 2 inner wires. I have continuity between the outers, but the center prongs seem to be open.
This is the thermostat I mentioned, it has a heater built into it.
The 2 outer connections are the contacts. Should be closed at room temperature (0 ohms)
The 2 inner connections are the heater. Should be around 6,000 ohms.
Try a higher resistance scale on your meter.
This could cause your problem but it would have to fail in a very unusual way (short to the case) and I would imagine the high current would blow it open.