Installing Python 3.3 on Cygwin
Building Python on Cygwin is not trivial -- I tried. However, the Python community on its bug tracker website is unusually friendly and gentle for a project its size and importance. If you find specific issues, open bugs and follow the discussion. Usually, they will accept tiny patches to fix Cygwin build issues.
This patch will solve your first problem about si->si_band. See related Python issue #21085.
This blog post (in German) is amazing. It will walk you through step-by-step how to build Python3.4 and fix all Cygwin issues.
Good luck. You will need it.