Phone started turning off randomly and would only turn back on when on the charger, as soon as it was unplugged it went off. I opened it up and ah-ha! The problem was the flex cable (is what I guess its called) from the battery to the board. It was corroded and when I tried to take it off it just split right in half, no force needed.
Ordered a new battery, got here a day before it said it would which please very very very very much!!! Just took out the old popped the new one in and it turned on by itself. I let it charge for a while after I turned it on.
I ordered the plasting opening tools and the spudger, but while they were cheap I don't think they were necessary, at least not for just changing the battery. You only need the screwdriver and your fingernail to unplug it!