I have a Toro, zero-turn mower, that won't even turn over.

Hi,
If it does absolutely nothing, and has a serviceable battery, it points to being a safety switch problem. The zero turn mowers add another dimension to switch problems as they have additional switches on the steering levers as a rule. Many also use relays in the harnesses to perform certain function.
Toro is very good about having parts breakdowns, operators' manuals and some service info on their site. Without model number and first digit of serial number, that is about all I can say.
Peace,
Clarke