Yes, it is a crash at startup.

I could not find XWin.exe.stackdump anywhere on my hard drive. I have
attached the bat script (renamed into .txt) used to start cygwin/X,
maybe I need to modify it.

Would it work to add 

CYGWIN='error_start=c:\cygwin\bin\dumper.exe'

in the system environment (meaning, via the control panel), to have a
core file that I could then open with gdb?