Wheelworks on W. 11th between Lawrence and Washington is the ticket. Take a look at the bikes on display and you will find the owner's Trek from the '70s; he's finally willing to part with it. (It's the very tall green one.) I bring all my '70s and '80s Treks in when I need/want something for them. Bill, the owner, and Kevin, the chief mechanic, are just great to work with. It's a small shop, so the stock on hand is limited, but they usually find a way...
The other shops in town are hit-and-miss, mostly miss. Steer clear of Paul's; they're bad news.
How about the DIY Co Op , on 1st near Skinner's Butte?
You're talking about the CAT (Center for Appropriate Transportation). They have buckets (literally) of parts that have been stripped from donated bikes that they practically give away. It's a bit hit-or-miss, but it is certainly a program that deserves more support than it gets. It's open from noon to either five or six on Tuesday through Saturday. The person who runs the show is really dedicated to helping at-risk youth find a niche in which they can make it. A good friend of mine used to teach high-school age kids at the CAT with the goal of helping them pass the GED.
Kevin, the mechanic at Wheelworks, worked at the CAT when he was younger.