First lets make sure your battery is good. Just because its reading 12+ volts doesn't mean its good. If you can get it load tested at a local auto parts store that would be a help. You could also try using a battery that you know is good, like your car battery or a Jump start box.
Second, as was mentioned by Rivets, check your ground wire. There should be a black wire that runs from the mower battery to bolt somewhere on the frame of the mower. The connections should be corrosion free and tight at both ends.
As you asked earlier about jumping the starter. Once you are sure the ground wire is making good connection, you can try jumping the starter. First remove the spark plug so you aren't fighting compression. There should be a thick red wire connected to a bolt on the starter. You can run a jumper cable wire directly from the red(+) terminal on the mower battery and touch the other end to the bolt on the starter that has the thick red wire connected. If starter spins the engine you know that it is working and we can look elsewhere for other problems.
Two things to remember...if the ground wire isn't making connection, this won't work. Second do this at your own risk. When you touch the pos(+) cable to the starter it will probably spark so use caution.
Get back to us and let us know what you did.