Check with a multimeter that L or N has a very high resistance to earth. If not, simply disconnect each part of the machine (heater, motor etc) until the low resistance or short disappears. Once the reading goes high, the problem will be the last item you disconnected.
If the resistance stays high at all times try disconnecting the heater but make sure you THOROUGHLY INSULATE the removed wires, then start the machine up. If the fuses don't trip you have found the fault. If they do reconnect the heater and disconnect a different part of the machine eg motor control unit.
As above, you will eventually find the fault. However, this does involve live working so please don't try to do it yourself to save some pennies unless you REALLY know what you are doing.
Colin, November 2007