Hp compaq presario cq35 problems!!

Hello,
Since yesterday, my com has a very strange condition. I tried to turn on my com with the charger plugged in and battery in, however it keeps turning off itself after on for a few minutes since yesterday. I tried numerous times and failed to keep my com on. However, I managed to keep my com on and work perfectly when I removed my bat from my com. When I used halfway, I put the bat in while charger was still plugged in, surprisingly my com just shut down itself. I checked the bat status before it blackout, it stated plugged in but not charging. my bat has damaged for once. This shows my bat is damaged, however, damaged bat will not lead to shutting down of my com. My com shuts down when the charger is still plugged. Anyone can help me? Helps will be appreciated.