The black, finned gadget in one of your pictures is the diode pack for the hazard light flasher.
The two un-connected terminals, the ORANGE & BROWN wires should connect to the hazard light flasher relay. The standard unit is the type that only has two terminals.
This however has no affect on the running of your engine so can be ignored as far as getting the engine to run is concerned.
In your other photos you appear to have the new, longer battery negative lead connected correctly, that is, between the battery negative terminal & the engine crankcase, rear right-hand side, inboard of the kick starter lever.
The thinner BLACK/YELLOW wire goes, I think, to the starter relay.
If you have not replaced that wire that might explain why the starter motor does not engage when the START button is pressed.
However, if you use the kick start lever to start the engine, providing everything else is OK, then the engine should start.
If the engine fails to start then you will need to do some fault finding & a multimeter is going to be your best friend here.
With the ignition switched ON & the KILL switch set to the RUN position there should be 12v+ on the two RED/YELLOW wires connected to the two ignition coils under the fuel tank.
You could also switch the multimeter to read resistance & connect one of it's leads to a good earth point. Then connect the other lead of the multimeter to the BLACK & the GREEN wires, in turn, going to the ignition points. As you rotate the engine & the points open & close you should see that reflected by the multimeter.
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