I went ahead and attempted to install GD on my Cygwin setup, and managed to get it running. You will need to have installed from Cygwin the following libraries: gd (ver. 2.0.36RC1-1), libgd-devel (ver. 2.0.36RC1-1), libiconv (ver. 1.14-1).

I'm wondering if you tried to add libgd to Cygwin from an outside source, since your version number doesn't match Cygwin's latest. Anyhow, give it a whirl and let me know how it goes. And, congratulations on your UNIX/Linux and Perl journey! I hope you find it as rewarding as I have. :-)