Door interlock is often to blame rather than the on/off switch. It contains a small heater which, when the machine is turned on and set to a program, heats up and causes a piece of metal to change shape. This in turn both locks the door and allows the program to continue - the time it takes to heat up explains the slight delay you used to observe between turning the machine on and the light coming on.
Sadly, this is rather a delicate mechanism liable to failure after a few years. I bought my last one from:
http://www.anglianappliances.com/
because they were handy, but you might find a cheaper source if you shop around.
I fitted it quite easily from the top on a WD61, I bet the WM51 isnt much different... there were two screws near the door catch that went though a white plastic plate into the switch behind. Make sure you note where the wires go! Oh, and there was a tricky little lip thing on the white plastic plate that made refitting fiddly.
J Skaife
April 2005