The problem is that crawl code is now using a newer version of the C++ language than before, and the compilers that come with msysgit are not compatible with that version of C++. So you need to install a different compiler package. This however leads to some other problems, which you have to get around by using certain make options. I wrote a short step by step guide below. If you have previously compiled crawl, you already did steps 1 and 3. There's no need to start from a fresh msysgit installation, but I had problems in the past that were likely caused by not updating msysgit for a very long time. So if your msysgit installation is very old, consider updating or reinstalling it.
1. Install msysgit, netinstall, preferably to the standard folder.
2. Download the compiler package installation thingy from
http://win-builds.org/1.4.0/msys-cygwin.html and install it into msysgit. To do this, just follow the instructions for msys on that website, but skip step 1. Don't use a fresh msys installation but instead run the exe you downloaded from an msysgit console. It will ask for your msys folder, it's the one you installed msysgit to.
3. To compile crawl you first have to obtain the source files via git, but if you compiled crawl before you probably already did that. If you didn't, follow the original guide for compilation in windows.
4. Because there are some new submodules you may have to run "git submodule update --init" from the repository root directory, even if you have previously checked out the submodules. Just do it once to be sure everything is there.
5. You are now ready to compile crawl. To do so you go to the "source" directory and use the "make" command, but you may need a few extra options. I cant give a minimal set of make options, but the following commands should work: "make BUILD_LUA=y" for console, and "make TILES=y NO_PKGCONFIG=y BUILD_ALL=y" for tiles.