04 350z driver side front headlight turning signal doesn't work but lights up.
 

Front headlight amber bulbs light up on both sides, when I turn on the headlights. However, when I activate the turn signal on the driver side (left), the bulb does not flash and inside the car, the turning signal on the speedometer flashes very quickly "hyperflash." Also, when I lock the car with the remote only the passenger amber light flashes, not the driver one. I am thinking its a bad bulb? Feedback please :)

I appreciate the responsiveness and helpfulness of the Z community. Thank you guys ! :)

Flashing fast on almost any car means burnt out bulb. All of those symptoms are from a dead bulb.