The program can't start because cygwin1.dll is missing... in Eclipse CDT

I've had Eclipse for Java on my computer for a few years, and decided to install the CDT and learn C. I installed both MinGW and Cygwin and the CDT detects and tries to use them when I make a new project.

I choose File > New C++ Project and choose Hello World C++ Project and the CygwinGCC toolchain. I name the project "asdf" and hit "Build Debug" in the toolbar. The compiler completes without error. I hit Run and nothing happens.

Browsing to the project directory manually and running asdf.exe gives me an error saying:
"The program can't start because cygwin1.dll is missing from your computer. Try reinstalling the program to fix this problem."

The same thing happens using MinGW, only a different dll is missing.
What do I need to do to have a usable .exe?
(I'm running Windows 7 x64 and the newest version of Eclipse and the CDT.)

EDIT: The compiler output is as follows:

**** Build of configuration Debug for project asdf ****

make all 
Building file: ../src/asdf.cpp
Invoking: Cygwin C++ Compiler
g++ -O0 -g3 -Wall -c -fmessage-length=0 -MMD -MP -MF"src/asdf.d" -MT"src/asdf.d" -o"src/asdf.o" "../src/asdf.cpp"
cygwin warning:
  MS-DOS style path detected: C:\Users\Shawn\Dropbox\eclipse\asdf\Debug
  Preferred POSIX equivalent is: /cygdrive/c/Users/Shawn/Dropbox/eclipse/asdf/Debug
  CYGWIN environment variable option "nodosfilewarning" turns off this warning.
  Consult the user's guide for more details about POSIX paths:
    http://cygwin.com/cygwin-ug-net/using.html#using-pathnames
Finished building: ../src/asdf.cpp
 
Building target: asdf.exe
Invoking: Cygwin C++ Linker
g++  -o"asdf.exe"  ./src/asdf.o   
Finished building target: asdf.exe

This error message means that Windows isn't able to find "cygwin1.dll". The Programs that the Cygwin gcc create depend on this DLL. The file is part of cygwin , so most likely it's located in C:\cygwin\bin. To fix the problem all you have to do is add C:\cygwin\bin (or the location where cygwin1.dll can be found) to your system path. Alternatively you can copy cygwin1.dll into your Windows directory.

There is a nice tool called DependencyWalker that you can download from http://www.dependencywalker.com . You can use it to check dependencies of executables, so if you inspect your generated program it tells you which dependencies are missing and which are resolved.

You can compile with either Cygwin's g++ or MinGW (via stand-alone or using Cygwin package). However, in order to run it, you need to add the Cygwin1.dll (and others) PATH to the system Windows PATH, before any cygwin style paths.

Thus add: ;C:\cygwin64\bin to the end of your Windows system PATH variable.

Also, to compile for use in CMD or PowerShell, you may need to use:

x86_64-w64-mingw32-g++.exe -static -std=c++11 prog_name.cc -o prog_name.exe

_{(This invokes the cross-compiler, if installed.)}

To add to this and save someone another google, just do this in cmd:

set PATH=%PATH%;C:\cygwin64\bin