Need new DS battery?

A few months ago my DSL battery died (for good), I've been playing my brother's DS but he lost it so I'm going to need to replace my DS battery, is this what I need; http://shoptemp.com/products/2000-mAh-Battery-Pack-for-Nintendo-DS-Lite-p-75.html

 

First off al, how do you knwo for sure its dead? mabey its your DSL?
How long do you have your DSL?

 

I've had it for about 4 years.

 

Just a question when did the battery died? when playing or after re-charging?

 

Hmm, it was a while ago so I can't remember very well but I'm pretty sure I started playing it when it finished recharging and then after a few minutes it died.

 

can it start because you play it with the charger in

 

No, it doesn't start at all, I turn it on, it shows the green light, the touch screen is completely blank and then after 1 or 2 seconds it switches itself off.