My BeagleBone Black does not turn on other than power LED turns on for a second
It is probably a power issue, or rather the lack of current. Try the following, or a combination thereof:


New USB cable
New power adapter
A different USB port
A different PC/Laptop
A different OS (Windows/OS X/Linux) - I have had issues where some boards work with Windows, but not at all with Mac - especially if it is a (Chinese) clone.


See also Element14 branded beaglebone black won't power-on. From there there are two getting started links:


Troubleshooting, and;
BeagleBone Getting Started


When you plug the BBB into your computer's USB port does it appear to be listed in the machines USB devices? According to the Getting Started guide:


  The first time you plug in the BeagleBone it will appear as a 'USB thumb drive' with the required drivers in the Driver folder (Windows, Mac OSX and Linux versions). (takes about 20 seconds)