I have never used Inline::C but this ...
LD_RUN_PATH=""
... jumps out at me. Also I don't know if
this is the case with Cygwin but I have ran into
problems on Solaris where my perl was a symbolic link to the
actual executable and I need the path to the actual executable
for some reason. If all else fails check out the cygwin
mailing list archieve. They (Cygwin) are pretty good
at fixing any problems users find.
Good luck!