Hmm. So you're saying that you electrocuted the cat and either left it electrified on the railing, or left it on the ground on its back, and then you quit the game and when you finally chose to launch the game again to continue...the cat was no longer there, and it isn't in your inventory?
If so, that's definitely a bit odd.
Yeah, I guess you might need to start over, or perhaps load an earlier save (if you have one).