By "changed the starter" do you mean you replaced the starter with a new unit? I did that earlier this season for the same symptoms: good battery, no starting.
Here are a few things I discovered in the process
1 - There was an inline fuse (20A) in the starter circuit near the starter motor, under the alternator. One of those black plastic twist off tubes that holds a glass fuse. This was in the wire connecting the panel button to the selenoid, but was intact and OK.
2 - There was *another* inline fuse right in the panel. This was hard to spot since it was just a glass fuse stuck in to metal clips which were soldered to short wires connected to a screw terminal on the key switch and (I think) the ammeter. just looking at the fuse caused one of the metal caps of the fuse to fall off and the panel went dark.
3 - The ground wire to the block can get corroded: moist area, dissimilar metals, etc. I took mine off and wire-brushed the block and lug till shiny and reassembled. This is the only path for electricity to flow from the starter motor (and alternator!) so very important that that's clean.
4 - The starter motor diameter is larger than the bolt-circle diameter of the two bolts holding it to the engine. There were small indents in the starter motor where a wrench or socket might fit, but I couldn't swing a wrench because of manifold on top and access on the bottom. In the end, I had to pull the motor body off the assembly to get access the bolt heads, and even then, none of my sockets would get to the bolts. I needed a shorter socket... At harbor freight I found some sockets that have little one-way sharp edges inside them meant for taking out worn/stripped bolts. These worked *amazingly* well at getting the starter motor bolts out.
5 - As mentioned, the Kubota price is 1/2 the Universal price. But the drop-in compatible clone price was 1/2 the Kubota price so I got the clone for about $90. One of the benefits of this newer gear-motor clone model is that there is plenty of space near the bolt heads for easy access with normal sockets! The engine turns over and starts so fast now it ia almost undetectable from hitting button to running.
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I think the inline fuse near the starter is standard factory issue. The one in back of my panel was unique though. The typical schematics show one somewhere in the starter circuit, but definitely not wired where I found number 2 there.
The quickest way to check the start wire circuit is to connect an alligator clip wire, first to the big + wire on the starter, then to a long screwdriver, then tap the energizing lug on the solenoid which should (with a spark probably!) crank the motor. Make sure you're in neutral first, or fuel shut off, or otherwise prepare motor to start running here. If that works your failure is somewhere between panel and starter. If first check the fuse(s) there.
After replacing the starter and putting a new blade-type fuse in for the strange glass one I found behind the panel (30A here) I'm starting much better now. That said, there was once last weekend I had to push the start+glow-plug a couple times to get it to crank, so I also suspect the aging switches are, well, aged, and probably due to be replaced. Also discovered I can start and run the motor without turning the key on which was a surprise, never had tried it before by my passenger did it. I don't think it would run long because the lift pump is powered off the key switch... but that was interesting. Maybe a side-effect of the strange fuse wiring I discovered? Another winter project.