You can find a OpenAxiom installer for Windows at:
http://www.open-axiom.org/download.html
More complete instructions for a full Windows setup without doing a build are here:
In the following order:
This package will install mingw-runtime, w32api, GCC, binutils and mingw32-make.
svn co https://open-axiom.svn.sf.net/svnroot/open-axiom/trunk open-axiom.trunk
Get the GCL source code:
$ export CVSROOT=:pserver:anonymous@cvs.sv.gnu.org:/sources/gcl
$ cvs co -d gcl-2.6.8pre -r Version_2_6_8pre gcl
Here are instructions to download and install the windows version of svn
Cygwin will give you a basic set of UNIX routines, such as ls, grep, etc., that run on Windows. Included is a Bash shell run via Cygwin.bat or its shortcut, both found in the main directory. Most other executables are in the bin directory. Cygwin has been around a long time and is stable. Installing it should not cause problems. More complete information can be found on the Cygwin site, but this is a quick start guide.