Samsung Galaxy S3 not turning on

A

AC Question

Just got a used Samsung Galaxy S3 and it was working before I bought it. It does not want to boot up past the Samsung Screen, it boots into recovery mood and the download mode then goes right back off. I have tried to plug it into three different computers but it always fails downloading the drivers, I have tried download the drivers from Samsung website but it still does not show the phone is connected. When plugged into the charger, it does not automatically start charging it only starts to charge when I turn it on and it only charges the battery to half way. After taking it off, the phone turns right back off and doesn't hold the charge very long.