All the smart and correct explanations have already been made, however, consider this:
The experiment has not changed at all, just the definitions did (slightly).
Now the question that cannot be answered until you open the box is no longer "did the cat die, or did the cat live", it is "did the cat die from the random poison trigger thing, or did the cat die from old age/starvation/whatever".
This can then be rewritten as two following questions instead, only answered by opening the box:
"did the random trigger thing happen (and the cat died from it)" OR "did the random trigger thing not happen (and the cat stayed alive)"
"did the random trigger thing happen (and the cat died from it)" OR "did the random trigger thing not happen (and the cat died by other means)".
The statements in parentheses are observations made by opening the box, while the statements outside are the information gained by making these observations.
If the observation part is removed, the questions become both the same (i.e., "did the random trigger thing happen?"), while the observed state of the cat is different by how the experiment is conducted, the thing that is uncertain until those observations are made is exactly the same, and therefore, the exact same "something that can be one or the other, but is unknown until it is observed" situation applies.
The cat is just an indicator of the state - if we change the way the indicator works, we are not changing the state in any way.
Therefore, the whole Schrödinger's cat experiment is essentially the same, although none of the possible outcomes are favourable for the cat.