Assuming the battery really is NEW, and fully-charged, most likely you have a poor connection at one of the ends of one of the battery cables. It could be corrosion between the post and the cable, a poor connection at the starter solenoid, or where the ground cable bolts to the tractor chassis. Also, sometimes the battery cable ends fail where the battery terminal end, or the eyelet on the other end is no longer tightly crimped or soldered to the cable inside, and there is battery acid and crud inside the connection. Make sure ALL connections are "clean, bright, and tight". If still no luck, take a test light, and connect one lead to the frame of the starter, the other to the battery cable stud on the solenoid. Then, press the starter button. You will see the test light flashing along with the solenoid's chattering, indicating you STILL have a bad connection somewhere in the big cables. Since you have replaced the starter with no improvement, it would seem to rule out the starter drive being jammed agains the flywheel ring gear, or a shorted solenoid or armature. So I think you WILL find the problem in one of the cables or connections.
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