It's possible that the connector between the screen and the rest of the computer has come loose. The first thing you have to do is check that the computer is actually still working. Is it making fan noises or noise from the speakers when you press buttons which would normally produce a sound? Does the caps lock key light up/switch off when you press it? If so then you'd have to follow the steps in this video https://www.youtube.com/watch?v=famBT6Tv... but instead of replacing the screen just slide the connector back in.
If you are fine with a bit of a hacky solution I have found staples are often quite useful for this sort of thing. If you have a stapler just staple nothing, collect the staple, and then unbend the prongs into the shape you need. Then just stick it in the slot and wiggle it about to try and lever the SIM card out. I think its unlikely you would damage anything since I don’t think the connections would be very sensitive.