A lot has happened since I first requested to send me MinGW build environment for building Git on this mailing list. Long story short, we now have a Git repo with MinGW build environment (msysgit) and automatic installer called GitMe that sets up build environment and source code ready for hacking.
Please consider joining our small team working on MinGW port of Git. To join go here: http://code.google.com/p/msysgit/, look around and then join Google Group http://groups.google.com/group/msysgit. There is plenty of work: http://code.google.com/p/msysgit/issues/list
-- - WinGit Team