It's very easy to take it apart without damaging it. Putting it back together after, now that's the trick.
It's not the membrane. It's the hammer retention mechanism. (I don't know of a better way to describe it.)
With keycaps removed, the hammer should have NO play and be up. That means if you gently grasp the spring and pull upward very gently, there should be
no movement. I wish I had some pictures to show it, but I haven't had to pop apart to that extent in ages. The default position of the hammer is always OFF (up) with keycap removed and there is no linkage between keycap and spring. It's an entirely floating assembly.
From what it sounds like here, your hammers are in fact resting on the membrane, which means essentially broken. It's impossible to determine whether it's the mounting plate (plastic assembly on top) or the hammers themselves without disassembly.