nofish,
It seems like the error you were having in cygwin is because cygWin is looking for a file in the RockBox Source code which isn't there (../rockbox/apps/action.c) and if the Source code was downloaded correctly, it should indeed be there...
That'd be the first thing to look at, the second being:
Did You make sure to set the cross-compiler paths in your ~/.bashrc file (not the only place to do this, but the preferred one)?
I had a similar problem with CygWin spitting errors at me on compiling, but stuck with trying to figure it out and now I can compile fine using CygWin (which I prefer over VMware...but that's personal opinion).
This is what *I* found I had to do:
From C:// I created:
C://Cygwin
In this .dir I created (*notice no spaces in the .dir's):
C://Cygwin/Cygwin_Application
C://Cygwin/Cygwin_Local_Package_Directory
C://Cygwin/SVN_Source
(file names should explain where I placed everything)
I downloaded CygWin and pointed the Setup to use the .dir's I'd just created but DID NOT download the precompiled cross-compilers from RockBox (the second time you run the CygWin Setup as per instruction in "CygWin with Screenshots"), but instead used the script ../tools/rockboxdev.sh which automates the process with the exception of setting the cross-compiler path.
On completion (and it WILL take a long time) rockboxdev.sh will generate the line of code that is to be added to the end of the user's ~/.bashrc file depending on which packages were installed by it.
If you installed all of them it's:
PATH=$PATH:/usr/local/arm-elf/bin:/usr/local/m68k-elf/bin:/usr/local/sh-elf/bin
export PATH
Edit ~/.bashrc using VIM or nano, not Notepad or Wordpad though.
It is important to note that rockboxdev.sh simply automates this procedure, it is not a different result.
If the cross-compiler directories were downloaded and extracted correctly, the end result will be the same.
The script simply removes some potential for user error during the cross-compiler installation.
If all went well, then I should see no reason why it shouldn't work.
[St.]
EDIT:
You'll need to download the Rockbox Source via SVN *before* running ../tools/rockboxdev.sh as it's included as a part of the source code, not as a part of CygWin.
Also:
In the "Package Selection" portion of the install, make your life a little easier by checking the boxes for nano or VIM, and either Curl or Wget (or both, or all).
EDIT:
There wasn't any spaces in the route to the build directory (or any cygwin .dir) was there?
Does/did CygWin have the approprate permissions to access the rockbox source .dir on your system?