I used cygwin to compile a .cc file, which runs fine in cygwin mode, but in windows/dos i get an error that cygwin1.dll not found -- although cygwin1.dll is indeed in the cygwin/bin folder.
Are you saying you're trying to run your cygwin program under the "Command Prompt"? I'm not sure that will work without some tweaking in your DOS/Windows environment. You might make sure that cygwin/bin is in your PATH in the DOS/Windows environment. If this doesn't help, try the documentation found at http://www.cygwin.com/.
Copy the cygwin1.dll from the cygwin installation to your programs folder.
Alternatively, it might be possible to statically link it but I don't know how.