We've got an old Bianchi "Forza" with a combination of the classic light green, and a sort of opalescent white for the downtube and stays. It's not a collectors item, but has been in commuting service for some time, and has a lot of that black gunk that comes off the brakes and rims. That stuff seems intractable. I've tried a number of different things to remove it from another bike of similar age, no go. I don't want to try anything that will attack the paint.

I hope this is appropriate to ask here. Is there a way to clean up this bike? It deserves to be a pretty bike.