Samsung Galaxy sIII Vibrates when charged for a few minutes, then just lights up topic

I found this phone in a parking space with an otter box case on it. Now it was probably ran over because the LCD is cracked and doesn't turn on (no hdmi-out to test that) but I was thinking I could fix it. When I plug it in, it just vibrates at even intervals and doesn't shut off. When I try to enter into recovery it stops vibrating as long as I'm holding the buttons, and then starts again as soon as I remove my grip. After waiting a bit, a blue LED showed up for a minute or so and the two bottom buttons lit up. Right now I have it charging, and when I click the power button those lights go on temporarily. Pressing the volume buttons, they make noise and light up.
It seems like it works, but is it worth fixing? Is there anything I should do to troubleshoot it? What is the vibration?
This is a new battery I bought online.

Regards,
Myles