perhaps i missed something in the AIR documentation or don't have a strong enough knowledge of Windows security, but it seems that executable files on Windows can not be launched from any directory other than the applicationDirectory.
launching the .exe from the applicationDirectory works. (tested on Windows XP and Windows 7)
I expect this is probably caused by myApp.exe needing admin priveleges to run.
Unless you need to read the apps outstream, the easiest way to work around this will be to call the application with File.openWithDefaultApplication() which on a desktop application will create the process with the required admin privileges.
Alternatively, the work-around is to call myApp.exe via another small program that can create the process with the correct privileges (like cmd.exe)
Tried using your code with the application Directory and I can't get my exe to launch. Were you able to get it working if you used the app directory? Below is the code... and error message.
var myApp:File = File.applicationDirectory.resolvePath("Hazards.exe");
var myAppProcessStartupInfo:NativeProcessStartupInfo = new NativeProcessStartupInfo();
myAppProcessStartupInfo.executable = myApp;
var myAppProcess = new NativeProcess();
Error: Error #3219: The NativeProcess could not be started. 'Not supported in current profile.'