External power supply not working (Leonardo)

The code is not the problem, it's a simple blink LED sketch.

I tried to use the 12V/750 mA power adapter from my YAMAHA keyboard: the Arduino worked and loaded my sketch. Are the other adapters I used broken or of poor quality? I don't get it ...

And the 9V battery still doesn't work: I exchanged the power supply jack with a new one. Maybe the battery is also of poor quality? (I attached an image.)

I'll try that thing with the multimeter later.