Brake and battery light doesn't turn on when I start the car

[donguaren]

I went to a store, parked the car for almost half hour, and when I put the key in ignition the brake and battery light did not turned on (like the others lights in the dashboard) and there was a new noice, like a buzz from outside the car (it wasn't loud, to someone who has never driven the car wouldn't have notice it) when I got home I turned off and on the car, still the lights won't turn on.

 

The car ran fine before and after, I did not felt a lose in power or something. The drive was short, like 4-5 miles total.

[donguaren]

To update, it was the battery that couldn't hold charge. I charge it with another car, the car started fine, but when I tried to start it again the battery was dead again. I put a new battery and it ran fine, started without problems.