Is the motor housing plastic? As the decades go by, they can turn darker, some tur horribly yellow. There is probably some kind of vent and heating action going on there that makes the dirt gather and escalate the problem. If the housing is plastic, I have read about ways of bleaching it with peroxide solution and some type of thickener to make a gel or paste of it. It might clean up much more easily though. I have put plastic covers like that in the dish washer a few times, it cleans them very well, but some plastic can't take the temperature, so it's a bit of a chance to do it.
There's a Yahoo Group called
Bernina Thirty Somethings, it's a very good place for all kinds of help with these models too. I have a 730 Record, my favorite zigzagger, it's very similar to the 830, slightly different knobs and exterior, but the functions and inners are very close.