Yes, it sounds like your MOSFET is fine.
It should be open circuit when the gate voltage is zero.
When you touched the gate with the positive probe, you charged the gate capacitance, which meant it conducted, when it was connected between the positive and negative probes. Shorting the gate, discharged it, causing it to become open circuit again. This isn't the most reliable method of testing, since some MOSFETs contain protection circuitry, which will discharge the gate. It's better to use another battery, to turn it on, although your method clearly worked on this occasion.