If 'getting KDE to run on Cygwin' is the objective, then toloban's got the right direction. But Cygwin can run WindowMaker and some other stuff easily. And if this is a 9x machine, ZipSlack will run a better Linux than Cygwin, since it's an actual Linux with a UMSDOS filesystem, whereas Cygwin's a sort of API. And then there's installing a full Linux on it's own partition. It all depends on what's the actual objective. If it is itchy fingers and the end result, time, and effort isn't an issue, might as well try to compile KDE for Windows.
If it's to actually run KDE, ZipSlack or a fully native Linux would be a better route. If it's just to have a Cygwin GUI, WindowMaker or something would be better.