The computer analogy wasn't mine, and I won't debate whether that's a good analogy.
Try this analogy. Think of it as a steak. If you take a dead piece of cow flesh and place it on the counter at room temperature, does it immediately turn into a goopy mess? No, of course not. The structure remains very close to the original tissue for many many hours. It doesn't matter that the cells are dead. It's the structure that we care about.
To take my steak analogy one step further, imagine that the steak was very fresh off the cow. As it turns out all the cells would still be alive. Even if you leave that meat sitting on the counter all day long, you would still be able to remove individual cells and grow them in a petri dish. They survive for many many hours. Even brain cells can be found living 8 hours after death. It's also common knowledge in organ transplants, for example, that the cells don't just die immediately.
But I think the biggest issue that you don't understand is that death is simply not black and white. It's many shades of gray. I've already pointed out that the cells are still alive. But even cell death has many shades of gray. Many enzymes can still be quite functional. The machinery is still grinding away. It is, after all, only a soup of molecules. They don't know anything about "life" or "death". The terms life and death are entirely man-mand inventions. Is a virus alive? Nobody is quite sure. How about a mitochondrion (that's the organelle inside a cell that generates energy). It's essentially a bacteria with its own DNA. It obviously 'does' lifelike things and is fairly autonomous. But it can't survive outside of a human cell. Is it alive? My point is that there really is a very big gray area between "alive" and "dead". The is DEFINITELY NOT a sharp line where something is dead. This is well known by all scientists.