I updated the FO project and rebuilt it but once I run the exe it crashes almost immediately.
What version did you have before updating, and were you able to build and run before doing the update?
It does throw some exception but I can't see it.
Run from the command line (cmd.exe) to see text output after crashes.
Is there any log for CTDs?
Depending when the crash happened, there could be something in the standard log files: freeorion.log or ogre.log in C:\Users\Username\AppData\Roaming\FreeOrion
Anyway the compile page said that I should rebuild libpng in the occasion of such CTD. This led to zlib problem.
That's one possible cause of a crash. Are you using MSVC 2008? If so, you shouldn't need to recompile zlib and/or libpng; the versions in the SDK should work.
If you're using MSVC 2010 and have never compiled and run freeorion successfully, that might be the issue. The log files or the text of the exception on the command line might help with that.
It starts to compile it and this is what happens.
It looks like there's a problem with the zlib project files then. Try removing gzoi.c from the zlib project (not the libpng project).