L293D motorshield with batteries doesn't power Arduino
The problem was that the 2 pins on which the jumper sits, the jumper or the board was broken (idk exactly). I might've caused that myself by turning on the batteries + powering it through usb at the same time.
I bought a new L293D board then made sure I didn't connect usb power to the arduino while the L293D was sitting on top of it. I uploaded the code, then disconnected the usb, put the L293D on top, powered it all and it works like a charm!