I tested that, and this doesn't seem to be the issue.
This theory wouldn't explain the following:
After I upload the sketch everything works fine, the power supply being the usb connection with my computer.
If I disconnect the Arduino from the computer and plug it back again, nothing happens unless I open the IDE and start the Serial Monitor.
From what I understand, when the Serial Monitor is started the Arduino restarts, so I tryed pressing the reset button after I power it ... but still no luck..
I also took into consideration that there might be something wrong with my microcontroller, so I changed it ... but I got the same result.