The screws are old and can no longer be screwed out

That's quite the predicament. The first idea I had is to just take a small drill bit and grind away the screw. You might also try sharpening a small flat head screwdriver (Ideally not a nice one) and then hammering the blade into the remaining screw. That could give enough of a recess to remove it with the screwdriver. Either way, you need new screws. I would replace them all, even the intact ones, just in case the rest have the same issue down the road. You could also try removing every other screw, if the rest work, and then rotate the shell off of the broken screw, but this could possibly damage internal components, and you'd still have a broken screw in there. You could conceivably take that out with pliers at that point, but it wouldn't help much if you couldn't get the case off. But anyway, good luck!

iFixit actually has a guide for removing stripped screws.
Wie man eine rundgedrehte Schraube entfernt
Be prepared to buy new casings; you probably won't be able remove the screws without cutting the whole casing apart.
I usually just drill through the screw head to remove rusted or stripped screws, as it does less damage to the outer casing if you're careful. Use a thin drill bit, as thick as the screw head, and take care not to drill too deep as you might damage the motherboard. You'll need to find some way to remove the screw stubs, though, so choose whatever method you like.