Debra,
Unfortunately there are a few things that could be wrong, but I would start with the on/off switch. I have no idea what your technical abilities are, but if you can get access to it and use a multimeter set to Ohms, you can check if the switch (unplugged from the outlet please) to see if you get a different reading other than infinity when the switch is in one of the on positions. If you do, then I would check the motor brushes (which are under those screws on the side). There should be a spring in there that has to be properly aligned with the brush that pushes against the motor rotor itself. If you say that you took them out and cleaned them, I would suspect you maybe didn’t put them in with the springs properly aligned. And they should be cleaned with electrical contact cleaner (not soap), so go buy a can (an auto parts store would have some) and re-clean them, if needed, then carefully reinsert and see if that helps. The mixer is old enough, you may need to get replacement brushes and springs if they are worn far enough where the spring that pushes them in isn’t “springing” any more. Hope this helps.