Should a grounded case have voltage across it?
The reason why you measure an AC voltage on the box when you have the box/housing grounded might be stray currents. 

Your multimeter has a very high input impedance and thus it displays such voltages from stray currents. If you put an oscilloscope probe on your desk and do not connect it, you might also see some 50Hz AC voltage on the oscilloscope display.

You can test this theory: Put a 100k Ohms resistor between your multimeter terminals and measure again. 

If you still see a 240V AC display, then there's definitely something really bad. If you don't see any display anymore, then you know that this came from stray currents and it is totally harmless (because stray currents have extremely high output impedances and thus no driving strength).