Each channel of the MP3 player has a live signal wire and an output ground wire.
The input to the VU meter circuit is the live signal and the input ground (at the lower left on the schematic) is from the ground wire of the MP3 player. Use shielded audio cables.
Without an input signal:
1) Measure the voltage at the base of the transistor. It should be 0V.
2) Measure the voltage at the emitter of the transistor. It should be about +0.65V.
3) Measure the voltage at the cathode of the diode. It should be 0V.
When the input of the LM3915 is 0V then no LED should be lighted.