PSP 3001 problem

Hi,I got a Malaysian friend to help me buy a PSP 3001 from Malaysia,which can play downloaded games on 8 June 2013.This is what happens.While playing my game,my PSP suddenly turns off in not the usual way of showing the "low battery" icon,blinking,before it turns off.It just shuts off.I tried to charge it through AC Power adapter.When I looked at the "battery information" while charging it,this is what I see:Charge Level: -
Hours Left: -
Power Source:External
Hours Left: -I continued to let it charge.Then the orange light goes off after a few minutes.I unplug my PSP from the extension cord and tried to switch my PSP on.It turned on for awhile before it shuts down again.It is when I take out the battery pack and plug my PSP to my extension cord,the PSP is working fine.May I know what happened,and what should I do?And of course,previously the battery seems OK,though the "Charge level" seems a bit weird,which I kinda ignore it.Weird as in it shows that the charge level is above 30%,even though I just used up the charge inside and start charging it not long ago,so it can't be charged above 30% in a short time.After my PSP is fully charged,then the "Charge Level" shows a 100%.My Battery Pack model is PSP-S110, 3.6V, 1200mAh, and I didn't open up my Battery Pack at all.On a side note,I also tried to switch my PSP on after the orange light goes off without unplugging my PSP,and it doesn't turn on.I also tried switching it on while the orange light is on,then it turns on,for awhile.

Replying to #1

This is a sign that the battery itself isn't holding any charge at all.Long story short, you got a busted battery pack.You need to buy a new battery if you want to use your PSP.Or you can do what I did when that happened to my battery. Try not using said battery for at least a month. After the month has passed, try using the battery in your PSP again. If it turns on, great, if not, let it sit out for another week or so. Rinse and repeat till it manages to power up, or it doesn't.

Replying to #2

Do I charge it first after a month is gone?

Replying to #3

If it doesn't turn on when you put it in your system.

Do I leave my Battery Pack outside of my PSP or do I insert it into my PSP?Oh,may I know what do you mean by "rinse and repeat till it manages to power up, or it doesn't"?

Leave it out so it would discharge on its own.And by rinse and repeat, I only meant continuously do that one thing repeatedly in an extended period.

Is buying a 3rd party Battery Pack* safe?As in,will it last or not?They are a lot cheaper,with larger capacity,like 2400mAh,but I kinda scare that it'll spoil easily,if my current Battery Pack will not be able to be charged and work again.*Those Battery Packs were not made by Sony.