need help compiling for Windows

["Sheryl Canter" <sheryl at permutations dot com>]

I've been trying all day to compile GCC for Windows, and I just can't do it.
I'm using the MinGW compiler as a boot compiler and cygwin for the
environment. I added c:\mingw\bin to the path, but I keep getting this error
message:

c:mingwbingcc.exe: not found
*** The command 'c:mingwbingcc.exe -o conftest -g   conftest.c' failed.
*** You must set the environment variable CC to a working compiler.

I don't know why it isn't showing the slashes in the path. When I type "env"
at the shell prompt, the path is correct.

What am I doing wrong here? I'm wasting hours and hours and getting nowhere.
Do I need a CC environment variable? If so, please give me the precise
syntax. I have no experience with Linux.

Thanks in advance.

    - Sheryl