Hi Agneta Dalväg,
Thank you for reaching Microsoft Community. We appreciate for sharing your concern to us.
I am aware of the problem you're facing with your Surface Laptop SE, which won't turn on when you try to start it. Let me help you on this.
Make sure your Surface is charged and disconnect any accessories.
To start your new Surface Laptop, Press and hold the power button until the logo screen appears (about 300 seconds). If nothing happens when you press the power button, make sure that the device is charged or plugged in to a power source. If the power connector light doesn’t turn on, or if it flashes, see Surface battery won’t charge or Surface won't run on battery.
Let me know how it goes.
Kind regards,
Lavenia