Okay, you need to know the battery is a good battery first, charge it or use another battery. Battery needs a load test not voltage tester to see if a cell is gone or it needs charge. What is the voltage across the battery terminals.? A good one should be about 12.6-12.7 volts. You said you havent cleaned terminal connections so you do as Wolfman says to clean all terminals, this means the inside the round terminal holders of the battery leads and the lead battery posts as well. If there is corrosion on them hot water and then sandpaper them, If they are the type with bolts through the battery posts then take them off and clean them. Take the nuts off the starter and clean the lugs going to it and the solenoid, also the nuts and any washers should be cleaned with emery paper or wire brush.
Then tighten firmly but not overtight. If there is an earth clean it also. I dont think there is an earth, I think the starter motor earths at the casing but I will check mine tomorrow. Does anything get hot or warm when you are trying to crank it? Do all this first, If there is no crank then it might be the solenoid connections or the starter, but since you had this overhauled its probably a bad connection or a terminal has some paint on it or something. Dont start ripping apart the starter until you are sure everything has been check for conductivity load test and voltage. This is a simple thing to check properly first. You should be able to see volt meter when you are doing screwdriver crank. But voltmeter only tells you so much, battery load test or another battery to try first.
P.S. I didn't read that you had a jump starter booster. These dont always work as they rely on good connections also. You need to be sure the jumper has a full battery also. I will look at my tractor tomorrow for you and send you some pictures of the starting system