LED's flash with music
Odds are that Q1 is smoked. You forgot to add a current limiting base resistor to limit the current. 

You should probably add a reverse diode on the base (after the resistor) to protect the transistor. The diode is recommended because you are feeding the base with an alternating voltage that swings above and below zero volts. When it swings negative the base-emitter junction is reverse biased. It will probably survive given that you are operating on a low voltage but it's good practice anyway.

Test the transistor with your multimeter diode test function. You should get 0.7 V b-e and b-c with + lead on base. You should get high reading when leads reversed.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Modified circuit.

When you get Q1 going again the next problem will be that you'll probably smoke the LEDs. You have no LED current limiting resistor in your schematic. You might get away with it if your supply voltage is low.

Edit: I couldn't read the supply voltage. I now see it's only 5 V. That won't be enough for four LEDs. As others have suggested, try them in parallel pairs.