PSP 3600 MaH Battery Problem.?

I recently bought a psp 3600 mah battery for my psp about 2 months ago and now I have a feeling that its life has already ended. Now, when I go to charge it like I usually do the charging light comes on and it seems like it's charging until the light shuts off and the psp wont turn on. I know it is not my psp because if i take the battery out and plug it in it works fine but i can't play unless the battery is out and i am not physically charging it. Is the battery done for or could it still be my psp because the system keeps restarting itself every time it does turn on.Meaning that i have to reset the date and time, etc. What can I do to fix this? Do I need to buy a new battery, most likely a regular one? If you have any more questions just put them in your answer. I'm giving best answer and if it works I will find you and pay you 1 trillion dollars. just kidding, but I will be very thankful.lol