Unless your DVM generates a voltage higher than the peak rating of the MOV (unlikely occurance) the MOV should appear to have a very high resistance if it is good or open.
I have never seen a MOV fail shorted -blasted to little bits sometimes but not shorted.
I was reading some reports on ehow (hope im allowed to say that) that these devices that are connected across LN,LE,NE will shunt, causing internal fuses to blow, thus protecting the equipment. In this case an air conditioner. Which in turn was protected by a 30mA RCD, so if this theory rings true, then the internal fuse, and RCD would open, and stay open? Which I do find rather bizzare if thats the case.
I await your expert advise.