Do you have a volt meter? If so can you measure the voltage coming into the board from USB? VIN(or VUSB) to GND... i.e to both verify that you are getting power and something is not screwed up with the voltage coming into it...
Also helps to mention things like you are running Windows (from photo), 10?
Is this a brand new unchanged board? Or did you do something like solder on headers? If you have soldered something on, double check for shorts...
I would also suggest a much more modern version of Arduino! I believe you are using Arduino 1.0.6? Try installing 1.8.9 (Current version) You don't necessarily have to overwrite your 1.0.6, you can download teh windows zip version, and unzip it to a different folder. In my case I unzip into root of d: driver so I have d:\arduino-1.8.9 ... I use D: on my setup as I have a smaller SSD as c: and a large hard disk d:... But again where here does not mater. Then you can install Teensyduino and point it at which ever directory you unloaded into.
I would then try to install a simple blink program... One of the examples... Sometimes I edit it first to change timing so I know it is running the one I changed.
Then choose board type as: Teensy LC, USB Type: Serial. Choose the verify command. Then hold in the program button on the TLC and plug it into USB. So the board should be forced into program mode... Then if necessary press the program button again. Does the Teensy program show it uploading to the board? Does it blink....
Might check to see if the device shows up as a HID device if you press the program button...