> LINK : fatal error LNK1181: cannot open input file 'advapi32.lib' 
> Error during linking
> 
> I put this file on my PATH, but then I get the same error. I don't 
> know how to fix it.

IIRC it needs to be in %LIB%, not %PATH%.

> On to cygwin... I've tried recompiling and installing ocaml from
> source, but that doesn't fix the problems.

Which problems?

And did you try simply installing the binary package available through
Cygwin's setup.exe, before you moved on to attempting a manual build? It
worked out of the box last time I tried it.

> MinGW version of ocaml...
> 
> ocamlc -custom rpn.ml does not have access to gcc, which is in cygwin
> only, so it doesn't work.

I've never used the MinGW version of OCaml, but at a guess, it might
possibly be expecting to find the MinGW version of gcc rather than the
Cygwin version.