Hi Calin
Please post the Arduino program you are using. Use the code tags when you create your post - use the "#" button above the row of smileys.
And have you connected your Arduino and the other components exactly as shown in the schematic on the page you linked to? It is hard to tell from the different angles, but some of your leads to the LEDs seem to come from Arduino pins different from those shown on the page you linked.
Unfortunately, only 2 of the 4 LEDs blink and I get no sound unless I touch the 2. Only then do I get only the sounds attributed to those LEDs.
Touching the LEDs (if that's what you meant) should not affect the sound at all. It may suggest you have a wiring problem.
Regards
Ray