I've unscrewed the screws that keep it to the case.
I gently pulled it and half of it came out, but now it's stuck and I can't put it back in.
No matter how much I push on the lever thing nothing happens and now my card is stuck. What do I do?
by the photo you posted it seems to be stuck at the PCIe Latch. Either the latch broke and not releasing or you need to try in install the GPU card until the gray latch pops up in the secure position and then push down on the gray latch again and see if it will release the GPU card.
Trying gently playing with the Gray latch and see if it will release the GPU Card.
very carefully see if you can pull the GPU card away from the latch. If you meet any resistance stop.
This Tech site thread a User has the same issue you now have with a stuck GPU card: https://linustechtips.com/topic/1028222-gpu-stuck-in-the-pci-e-slot/
The above link give some tips on how to unstick the GPU card from the PCIe slot.
From a Tom's Hardware Thread concerning the same problem: https://forums.tomshardware.com/threads/gpu-stuck-in-motherboard.3570909/
I've done that before, lol! If you gently lift the back of the card where it's nearly touching the board and at the same time sort of push forward/down on the top/front of the card, gently as well, the front should drop a hair and the back clip will be moveable. Another way is to grab the raised part of the card and push forward/down, like you're installing it but not too hard with one hand. Use the other hand to knock that clip back and it should come free. In any case, no major deal if the rear clip breaks but try not to! Do not wiggle the card side to side or you'll spread the contacts for the slot. Good luck!