Problem with RF transmitter/reciever and VirtualWire
The problem seems to be rather banal.

You forgot to properly set:  

pinMode(13,OUTPUT);


in the setup() function.



Incidentally, your code should actually be working, with the exception that the LED state is likely constant. It should be transmitting anyways. 



Further Edit:

Ok, I've dug into the virtualwire library a bit more, and I think I see the problem

Mainly, the default configuration for the VirtualWire library TX pin is pin 12.

Basically, you have connected the transmitter to the wrong pin (in the pictures, you have it connected to pin 1).



Adding a TX activity LED to the module:

 

Note that this will only work properly with vw_set_ptt_inverted(true); commented out.