I had a system that that happened just the other day and I didn't know it until the latch broke off. The latch broke off and that was it. It was one of those sliding latches on an ASRock mobo. I guess I didn't need the latch anyway
I'm not saying you should break yours. I would try to remove the latch from being stuck. Maybe use something besides your fingers, such as a flat screwdriver, to push the latch out. But that could get dangerous if you slip and damage the motherboard. Idk..
What kind of motherboard is it?