For me, it's more helpful to have executable code to go through the process, so I'm going to put some in. This is addressing your concern,
I suspect it is something with how/where I installed the compilers...
because the installation from apt-cyg should be helpful in letting the system know where to look for the compilers. I'm also addressing a possible linkage issue.
bballdave025@MY-MACHINE /cygdrive/c/bballdave025 $ apt-cyg install gcc-fortran libgfortran5
If you don't have apt-cyg yet, follow these instructions from another answer.
# Get to where your setup executable lives. # This is what you used to install Cygwin the first time. # Note that mine is for the 64-bit version, and that # I keep mine in C:\cygwin64. Your path might be # different. You also might need to re-download # The setup executable from Cygwin. $ cd /path/to/setup_install/setup_x86-64.exe -q -P wget $ wget https://raw.githubusercontent.com/transcode-open/apt-cyg/master/apt-cyg $ chmod +x apt-cyg $ mv apt-cyg /usr/local/bin
The libgfortran5 (or a more recent version, if available when you search) might be necessary. Here's why I think this might be the case.
bballdave025@MY-MACHINE /cygdrive/c/bballdave025 $ man gcc | grep -A 3 "[ ]*[-]l[ ]\{0,2\}library$" -llibrary -l library Search the library named library when linking. (The second alternative with the library as a separate argument is only for POSIX compliance and is not recommended.)
(Note that I haven't included some parts of the result that aren't useful and can be fixed by prefixing the command with MANWIDTH=160, cf here.)
There is a little more detail and a little different result from the answer to a question about the lib prefix on files:
You can name a library whatever you want, but if you want gcc's -l flag to find the right one, you need to name it the way that link describes. For example, gcc -o myapp myapp.c -lm, [w]ill compile myapp.c, link the resulting object with libm.a, and output an executable called myapp. These days, there might be a more complicated search path involving dynamic library names, etc., but you should get the basic idea from this example. [In addition, you can look at this section f]rom the gcc man page:
-l library ...
... surrounds library with lib and .a and searches several directories.
The basic reason for all of that info is this: it is very possible that, in order to link with the gfortran library, you need to have installed a package named something like libgfortran. I don't know for sure how this works, especially with the Cygwin man page being slightly different, but it's worth a try. The likely extra thing you would need in this case is something like
apt-cyg install libgfortran
or
apt-cyg install libgfortran5
Here's some helpful info on how I found what to install. When I had a similar problem, I went to the Cygwin package search, but I only got three entries with three versions of netcdf-fortran

(archived). I wanted gfortran, so I kept looking
I found a great gfortran answer in this SO answer. With that answer, I went back to the Complete Cygwin Package List, armed with my trusty Ctrl + F, since I knew there were packages different from what came back from the search. The complete list had
cygwin64-gcc-fortran GCC for Cygwin 64bit toolchain (Fortran)`
gcc-fortran GNU Compiler Collection (Fortran)
and entries for libgfortran.
Hopefully some of this information will be helpful, or at least educational.
checking whether the Fortran compiler works... nobefore the error? It would be more informative if you displayed the whole config.log.config.logis really necessary.