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That usually signifies that you either didn't set the right path or screwed up the install completely. The cc1.exe file is the executable of the compiler proper, don't delete it and place it in the path (or more common, move the path so it's on it).
Looks like you are trying to execute Cygwin executables from the Windows environment (not within the Cygwin shell). That may be complicated.
If that's the case, you should either use another compiler suite for Windows (djgpp could be one, though I never used it) or keep Cygwin and learn to use make. make.exe will recognize Cygwin paths and will find your executables. Take a look at http://k101.f2g.net/ on Chapter 1.