Recently, I face some problems with my beloved DS.

Firstly, it is the left button on the direction pad that goes wrong. It is less responsive compared to the first time I pressed it. It is still usable but I have to press it harder than the other buttons. Next, it is the LED. The one that shows the battery life (yellow/red). I believe that every DS blinks according to a certain tempo (like mine used to) when it is closed while the system is still running, right? But recently, mine blinks a lot faster and makes a weird sound when I closed it with games running.

Sigh. Anyone faces this before? I wonder how much it will cost me to fix these problems...

That is certainly weird, the blinking part at least, your best bet is to bring it to a reputable store and ask the technician there directly.