First make sure that the mixer is plugged into a working outlet. Were there any symptoms the last time you used your mixer? Check the cord on the mixer for damage. If the cord shows any wear replace it immediately.
At any point in time have you removed the brushes or adjust the speed control plate? After checking the cord, remove the brushes from the mixer, check to see if they are pitted, if they are replace the brushes. Please pay extra attention when putting the brushes back in the mixer, there is a dog-eared side of the brush, match this up to the brush holder to make sure the brush is inserted correctly.
If the brushes are not the problem check the speed control plate. If you remove the end cover from the mixer you can gain direct access to the speed control plate. There are 3 screws on this plate, the top two are used to adjust the speed of the mixer, the bottom one spaces the on/off switch contact. Try adjust the bottom screw to see if the mixer will turn on, it is possible the on/off switch was out of place.
Try these first, if none of this works let me know and we can continue trouble shooting.
Here is a link to the cord for your mixer: http://www.mendingshed.com/mixercord2.html
Here is a link to the brushes: http://www.mendingshed.com/kitchenaidbrushes.html
Here is a link to the speed control plate: http://www.mendingshed.com/speedcontrol.html
And here is a link to the service manual for your mixer, it has more troubleshooting ideas on the last few pages: http://lib.store.yahoo.net/lib/mendingshed/kitchenaidservicemanual.pdf