The machine is not working when the switch is on - therefore it will not draw current. You may do better to look for voltage (and the absence of it) to determine the fault rather than looking for current, when, by definition, there is no current.
There can't be much to go wrong - Fuse - Cable - Switch - Overheat cut out (it it has one) - Motor - neutral return path. Of course there may be a broken conductor or bad connection in the device but it's very unlikely.
Find some way of checking for 230V - a mains tester screwdriver with a neon in the handle is cheap and effective. You mention mains voltage on the input side of the machine's switch - is there voltage on the other side when the switch is on? etc. etc.
You may have a damaged power cord that's causing the problem but any break will be in the neutral conductor as you've already tested the live wire. I have never heard of a conductor that passes current when there's no load but doesn't when there is load - apart from a fuse - and do not consider such a symptom possible.
Good luck...
Peccavi
May 2009