I've got the battery working completely right now. Thanks for all the support guys!
Though it still wont turn on. It only does something when I plug it in my PC.
Then the screen flashes for less than a second and the access indicator for the PS Vita game card flashes for a second. Then it sort of disconnects from the PC. Really strange.
I also called PlayStation and they said that I could send it to them and I could buy a refurbished one for 75 Euros. But I'm not going to do that. Then I could better buy a pre-owned Vita.
So anyone who knows what it could be?