Logsplitters are like chainsaws for homeowners, you only use them once in awhile, sometimes once per year. If you have fuel in it for long periods of time like that, you are going to have issues. Nearly all fuel at the pump has ethanol, which is hydroscopic. That means it absorbs water over time. Because of this you get two things that happen: The first is corrosion. The aluminum or steel components in the carburetor will corrode or rust. Carburetors are very fine things, the passages in them are easy to block. The second thing that could happen is the breakdown/ degrading of the fuel. Because of all the additives some fuel will begin to degrade over time and turn into a sludge or algae like substance. If either of these things occur it is unlikely the engine will start. Sure, it could be dirt in the carburetor but being that it has sat a long time, I would be willing to bet if you take that carb apart you will find the inside looks pretty terrible. It also doesn't help if it is being stored outside, that just adds more to the problem.
Things to do:
You know you have spark because you got it to fire from putting fuel straight through the barrel of the carb. So you can eliminate any electrical or safety components from the equation (i.e. low oil sensor, ignition coil, spark plug, on/off switch, etc.)
1: Pull the fuel line off at the carb and see if fuel is flowing through it. If it is, drain it all out and get new.
2: Take the bowl off the carburetor. If it is rusted, corroded or full of slime, take the carb off and throw it out, get a new one.
3: If rust/ corrosion or slime was not present, hook the fuel line back up and see if you are getting gas into the carb.
4: If you are, then more than likely the main jet/ emulsion tube is clogged. Get some very thin tag wire, shoot it straight up through the emulsion tube (the area the bowl nut threads into). The wire should go all the way up into the barrel of the carb.
5: If the nut has a small hole or holes in it, do the same to those.
6: Put it back together and see what happens.
It's also very likely the fuel in there has water in it which will more than not cause it not to run as well. Things are not how they use to be. Fuel is now full of additives that don't help carbureted engines, and the new engines are all designed to meet EPA standards so they have to use less fuel. It's the double edged sword. It's not uncommon to have issues with fuel one MONTH after purchasing it. Imagine one YEAR later...