Difficulties with the virtual wire library and 433RF

It doesn't default as an output. I tried this sketch:

void setup () 
{
  digitalWrite (13, HIGH); 
}  // end of setup

void loop () {}

I must admit that pin 13 glows very faintly, but that is because the pull-up resistor has been enabled. You should add:

pinMode (13, OUTPUT);

... to setup to see it more clearly.

As for your problem, checking the pdf file about VirtualWire, he seems to be talking about a transmitter (TX-C1), a receiver (RX-B1) and a transceiver (DR3100).

Now you said:

I have bought a 433Mhz transmitter and receiver ...

Not the transceiver, right?

But you have in your code:

    vw_set_ptt_inverted(true); // Required for DR3100

But you don't have that part.