If you're not a mechanic at all, your best bet is to get a mechanic to look at it. They'll have it fixed and you'll be plowing snow instead of spending weeks diagnosing the problem and sourcing parts.
I know nothing about your tractor, but there are some universal engine diagnostic routines. So, if you do want to take a crack at it yourself, read on.
You say "the key turns over and nothing, just dead, no oil light, nothing." When you say "turns over," people that work on engines interpret that to mean the starter is turning. Does the starter turn when you turn the key (That's the rrrrrr-rrrrrr-rrrrr noise that your car or tractor make when you're turning the key but they haven't started to run on their own yet)? Or do you mean that you turn the key and absolutely nothing happens?
If it's the latter, and absolutely nothing is happening, then you have an electrical problem. Double-check the connections at the battery. Also, look at the connections on the starter (It's a coffee-can sized electric motor hanging off the back of the engine. It will have a big wire going to it). If everything looks good there and the key still doesn't do anything, the first thing to check is the battery. It could be dead. If you have a multimeter and know how to use it, check the voltage at the battery (to make sure the plates haven't shorted out internally). Put it on a trickle-charger for a few hours and see if anything works. Better yet, try jumping the tractor. If it acts like it has power (Lights on the dash, headlights or work lights, or some other electrical accessory works but the starter still doesn't turn), then it could be a bad starter. You could try bump-starting it if you have something strong enough to pull it.
If it is actually turning over and the starter is turning, then you are on to the basics of gasoline engine diagnosis. Air, Fuel, and Spark.
You're getting air as long as your air inlet/filter or exhaust aren't completely plugged (full of snow, for instance) and you have compression. If you don't have compression, you're beyond any repair you're likely to do yourself. So all you can do is make sure the air inlet isn't blocked by anything. Look at the filter to make sure it's reasonably clean. Make sure there's nothing packed in the exhaust.
Assuming the "air" checks out, you're on to spark. This is pretty easy. Get an assistant to help you out. Find a fairly dark place. Remove a spark plug and hook the wire back up to it. Make sure you're not near any rotating parts and use a pair of insulated pliers to hold the plug wire so that the plus is millimeters from the engine block. Have your assistant crank the motor and watch for the spark. If you don't have one, it could be a bad coil pack or a bad ground somewhere.
If you have spark, then you need to check fuel. The easiest way to do that is to put everything back together and pull the air filter off the carb. Hold a propane torch near the air inlet, then have your assistant crank the motor. Open the valve on the torch so that the engine is sucking in the propane. If it stumbles and tries to start on that, then it means that it's not getting fuel otherwise. I don't know how the fuel system works in your tractor, but that could be a clogged fuel filter or a non-functioning fuel pump. It could also be plugged jets in the carb, but I doubt that's the issue if it was just running.