Battery not installed and won't charge

Hi, my MacBook 13" had multiple problems. I went out for a trip for a couple of days and when I came back the battery was swollen. I took it off and tried to power up the nb with only power cord but it won't turn on. I bought a brand new spare battery and now it turns on with magsafe's led in green and won't recognize the battery and after a couple of minutes it turns off automatically.

Anyone with same issues?

Thank you.