Samsung Galaxy s2 doesn't want to stay turned on?

Pleas help me.

My problem: Battery has 100% charged, but when I connect to charger, the phone screen turning on and showing 0% battery.

When I turn on my phone, it work just fev seconds and automaticly turning off, it happened when the charger is pluged in. When phone work these fev seconds, it shows no coverage, and Memory card error. But it steel not work without memory card, SIM and charger. My phone not crashed or water atc. I use it 3 years.

If problem is battery.. How it's possible that it doesn't stay turned on all time when charger is pluged in?