When you have just the USB cable plugged into the AxiDraw (please make sure that the power supply is NOT plugged in) does the LED labeled USB next to the power jack turn on? There is also an LED above the capacitor cutout labeled 3.3V. Does it turn on? (You may need to look upward through the cutout to see it.)
Are there any signs of damage from shipping, such as bent parts or loose connectors?
