I got this response from Trek today:

"I would start with the soapy water and some fine steel wool. There is a product you can find at Home Depot and other stores like it called Simple Green, it's a basic household cleaner and comes in a spray bottle. I use for my bikes (but dilute it somewhat) and it works well for general cleaning of the frame and wheels. You could definitely start with this, but if the shine and polish does not return to it replacement wheels for a bike like this can likely be obtained for under $100 through your local dealer, so it might not be a bad idea to have them inspect them as they would be able to make a recommendation as to how to proceed from there. "

I'm not going to replace the wheels but might take it to the bike shop. They charge $60 for a tune-up. Another shop charges $39.99. I don't know if that includes cleaning the spokes.