We will go through evaluating the board and then attempt to classify the types of problems. It is important to keep in mind that a perfect diagnosis is a difficult thing to do. The part with the LEDs can be partially done without any additional equipment. For the BeagleBone Black (BBB), a serial cable can provide a lot more details.
The first step is to observe the LEDs on the BeagleBone. A functional BeagleBone has a power LED light controlled by the hardware. Most BeagleBone system software will, by default, blink the other LEDs to indicate system activity. If none of the LEDs are on, check whether the power is switched on. It is especially important to verify that the BeagleBone is solely powered from the USB port. The USB specification provides up to 500 mA per port but, in some cases, this can be limited to 100 mA. The 100 mA current can cause the BeagleBone to boot and reset. Although 500 mA is available, the BeagleBone...