When I plug in the cord into the micro-HDMI port, there is no video output.

I just bought the camera, but it seems there is no memory card.

The colored LED light around the power button indicates the camera's battery status. Blue color means your battery is 100% to 50% charged. Purple means it is 50% to 15% charged; and finally, red means there is only 15% or less of your battery charge. You may need to charge it in order to use the camera.