Why does my tablet only stay on the start up logo?

My Galaxy Tab 3 had a broken charging port, but I did not take it to get replaced until about 7 months after it died. After getting it back, the tablet will only "turn on" if it is plugged into an outlet, it will not work if plugged into a computer. It will immediately turn off it is unplugged. Even though it is "on" it only stays on the black logo startup screen. It will not load. I have tried a hard reset, but it only flashes and returns to the same startup screen. I took it back to the repair shop and they looked at it and told me that they do not know what is wrong with it. They said if the battery was dead then it wouldn't be coming "on"... Is this true? It isn't necessarily coming on, but rather staying on the startup screen only when it is plugged in. When my laptop battery was fully drained of life, I could still use it when it was plugged in and the battery was removed. So I think that this could be a similar situation? Does anyone know how to fix it?