Cables, wires, connectors (including all earths) all need to be in good or reasonable condition all clean, secure and protected, For diagnosis of an electrical/electronic and/or starting problem you are best to have the 12v battery fully charged and in a good state of heath and connection(s) or at very least reasonable in all. As proven by the corrasion you have highlighted in your photo, corrosion like that in various places could be the cause of your problem - all needs to be clean, secure and protected (otherwise the corrosion may return)
All sensor need to be in good or reasonable condition and correct for the specific vehicle (or engine if engine change).
Just because a part is new doesn't rule out it possibly being faulty or perhaps incorrect for vehicle/engine. For cars of this age they can be fastidious about the sensors fitted.
I remember well an owner oh here having problems starting the engine (in very cold) and all other posters, including me, thought the starter motor sounded fine in his video but it was the starter at fault. Now I am not saying either of your starters are at faulty, I could not know over the internet anyway, but if the fitting or wiring to it, or anywhere else has an issue it could present this yes/no to starting the engine.
You need to do proper diagnostics, using your eyes, ears, nose, feel, taste, brain / common sense and use of any other diagnostic tools you can get or make. For electrics on starting the engine you could start at the battery and go forward from there, a multimeter would be handy (as might be a scan tool) but the previously mentioned diagnostics tools are needed regardless.
Another person with you might notice something obvious you have missed, often these problems can relate to something simple and basic that has ben overlooked or ignored or not checked, or not double/treble-checked or thoroughly enough. Something like a bit of crud/corrosion on the inside of a battery terminal clamp if missed will still play up even with a change of battery (and (I am not saying this is your problem, how could I).
Either follow previous suggestions or start a clear path of diagnostics and stick with that path and double and treble check as required and make no assumptions. There may be more than one issue combined or separately contributing to the issue so if you want to know the cause(s) then do not be changing more than one part at once and do not assume that an existing or replaced part was fully working correctly even if it was working or that it was fully correctly fitted. Check and cross -reference any existing parts are correct and working correctly, or not, before putting on a new same part and how it is fitted.
Good luck.