How to shutdown an Android mobile programmatically?

It is possible, but you need a Rooted Android device with Superuser access. You can't do it without Root unless your app is signed with the System Firmware Key. Try using the following code:

Shutdown:

try {
    Process proc = Runtime.getRuntime()
                    .exec(new String[]{ "su", "-c", "reboot -p" });
    proc.waitFor();
} catch (Exception ex) {
    ex.printStackTrace();
}

Reboot:

Same code, just use "reboot" instead of "reboot -p".

[On an other note: I read somewhere that these commands do not work on Stock HTC ROMs, but haven't confirmed myself]

You could possibly use the PowerManager to make it reboot (this does not guarantee that it'll reboot - OS may cancel it):

http://developer.android.com/reference/android/os/PowerManager.html#reboot(java.lang.String)

It requires the REBOOT permission:

http://developer.android.com/reference/android/Manifest.permission.html#REBOOT

Can you also check your logcat when trying to enable/disable keyguard, and post what's there?

You cannot do this from an ordinary SDK application. Only applications signed with the system firmware signing key can do this

This is the code i use to perform any system command.

void shutdown_sys()
{
    Process chperm;
    try {
        chperm=Runtime.getRuntime().exec("su");
          DataOutputStream os = 
              new DataOutputStream(chperm.getOutputStream());

              os.writeBytes("shutdown\n");
              os.flush();

              chperm.waitFor();

    } catch (IOException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    } catch (InterruptedException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    }
}

Call this function from your android App. It will work if su is functional in your system. Let me know in case it does not work. I dont have an Android base ready to test. But the same works for reboot. So shutdown is also a linux shell command which ithink will be there in Android as well.. All the best