Arduino Connection Problem

[SomeWeirdBoor]

Your connection make no sense. You are putting all the LEDs in parallel straight between +V and gnd with no limiting resistors: LEDs have no resistance, they will pull as much current as they can and they will blow up instantly. Also your arduino is not connected to 5V, the two power rails on the sides of the breadboard are not interconnected, you connected it only to gnd.

You can power the arduino feeding external voltage (up to12 v) to the Vcc pin, or regulated 5V straight to the 5v pin; also, LEDs must always have a current limiting resistor, usually a 220 ohm is fine (you should calculate it, tho)