Couple of things:
1. This schematic helps significantly: http://www.dfrobot.com/wiki/images/a/a0/RoMeo_Schematic.png
The manual for this thing is horrible. I think it is cute how they mention that S1-S5 are on an analog input, but don't bother to show how to use it or mention which Pin.
2. This Arduino varient takes advantage of the 2 (little know) additional Analog inputs provided by the ATmega, which is why A7 looks odd in the example code.
3. As noted, you can't PWM Pin 13. However a little known bug (feature?) of AnalogWrite is that if you AnalogWrite values greater than 127 to a non-PWM pin, it will write a HIGH. Regardless, you should be using digitalWrite(13, HIGH) for Pin 13.
4. Based on the schematic, S1 will return a value of 0 while S2 will return a value of 700mV. This means analog values between 0 and ~140 are probably S1. So you might change your "if-statement" to be:
if (analogRead(key_S4) <= 100) {
digitalWrite(LED, HIGH);
}