What is it you think doesn't work?
Actually, I think the only reason that you get some strange errors in
your log file is that the bug-lilypond-cygwin script hasn't been
updated since the documentation was moved from /usr/doc/ to
/usr/share/doc/. Try to run the following commands manually:
cp /usr
Download and ran setup.exe from your download site.
Ran setup.exe using all the options you suggest ( used
ftp://cygwin.csie.ntu.edu.tw/pub/cygwin as download source)
Tried to run the sample you suggest...didn't suceed.
Included is the bug.txt as you requested, and the two output files generated