Riding Lawn Mower Won't Start?

My riding lawn mower, a Murray model 40504x92, was running just fine and suddenly while mowing one day just stopped and won't start. I replaced the battery since it wouldn't charge up thinking this was the issue, but no luck. I tested the new battery and it's holding its charge at 12 volts. However, I am getting no volts on any of the wires on the solenoid when I turn the key. I do get a whine like the mower is trying to turn over. I don't know if this means if a safety switch is bad or the entire ignition is bad or I need a new solenoid. Please help. I am a woman trying to figure out how to fix something I shouldn't be fixing lol.