I haven't tried to connect it up to BricxCC, being a confirmed text-editor-and-command-line type; it works great like that BTW.
So I went back and just hit "all" when the Cygwin installation asks you to select packages, and then it worked, which is simple, but uses up a big chunk of hard drive, and takes a pretty long time to download.
Of course you can also do it the smart way and look at the list of required packages as well.
Finally, note that for some XP setups you have to manually add c:/cygwin/bin to the PATH environment variable. Otherwise when you try to run the script buildgcc.sh things like make can't be found by the system.
Several people in the class had serious problems installing BrickOS under both 2000 and XP, but there seem to be ways to fix them.
The collection includes a newer version of gcc, newlib, and the cross compiler for the Hitachi processor in the RCX, so this route allows you to avoid having to do most of the building.
This version apparently works okay.
There's some suggestion (in the howto) that there are RPMs for Red Hat users, but I haven't tried to track them down (yet). I know that there are issues getting the IR transmitters to run under Linux, and I'm delaying the pain until I have more time.
If you want to do an install from scratch, it shouldn't be too hard. From what I have seen of the build script that comes with the Cygwin installation, all installation requires is a reasonably recent version of gcc, so if you rewrite the script to set up the relevant paths or run the instructions by hand, everything should run fine.
In theory of course :-)