Welcome to the forum 
Hard luck. That’s certainly a situation where being unable to disassemble the phone is a disadvantage.
As a general rule probably it would have been better to turn the phone off immediately, even though you couldn’t open it straight away.
As things stand I think the best would be to test another screen before ordering a new one. If there’s a Fairphone angel near you who has access to a FP6, or knows someone who has, they might be able to help. Or you might advertise your general area in the hope that another Fairphoner reading this could get in touch, maybe by DM.
If you do manage to get the phone working again, I would think your immediate priority should be to ensure a backup of your data, if that’s not already done.