Hi. I've just been reading through both of your posts on this topic because yes, you guessed it, I am currently having the exact same issue. I apologise for this being so long but I need to get the setting right, as I'm sure most of this is familiar to you. So please bear with me and if anyone else can help I'll appreciate your input as well.
Over a week ago now I was out with my wife having a drive as it was beautiful weather for it. Anyway, we stopped at one tourist attraction and off we went to have a look around. On coming back to the car to set off for another destination we got in the car and then, nothing other than a click.
The car had power and was doing everything correctly except for starting. It wouldn't. I checked all of the fuses and at the time I didn't see any that had blown (I was wrong). So I then thought it must be the starter because everything else was fine (it wasn't of course). So I called up Green Flag to come out and have a look and see if they could help. He gave the same diagnosis as I had, the starter motor was dead (he did say he isn't an expert at all on the P38). Anyway, we had to call a towie to come get us and take us home. So after an hour or so of waiting and a further hour or so later we were back home and by then it was late so left it for the night. I asked around on forums etc and everyone I spoke to said yes that it definitely was the starter motor.
The next morning we went out to the car to see what the problem was. That's when I discovered the 40 amp fuse (position 40 I think) had blown. So I replaced it with the spare and tried it again and boom the car started first go and I was able to drive it from the front around to the back in our drive.
I thought nothing of it at the time and we didn't need to use the car again until a few days later.
A few days later I needed to run my daughter up to the nearest town for her to catch the train into the city. We all got in the car and were ready to set off. I turn the key and........nothing. Exactly the same as on our drive a few days earlier. So I looked at the fuses again and saw that the 40 amp fuse was yet again blown. Having no spares I had ordered some but they weren't going to arrive until the weekend at the earliest. That didn't happen and we only got them yesterday. The joys of internet shopping and living in a very small village. We don't even have a chippy. Go figure.
Anyway, I had also decided to replace the starter motor to completely rule that out, and given the original one was from March 2001 when the car left the factory and it wouldn't hurt to change it anyway and refurb the old one to keep as a spare. We needed to go for another run-up to town and while waiting for the suspension to rise I realised "duh the fuse is blown so it won't work." We then drove on bumstops (not nice) to the mechanic workshop down the road about half a mile to use his airline to raise the suspension (yes I fitted the bypass. He loved that setup btw and no he knows nothing about these cars. His words not mine).
So after I had received the starter motor and everything else I needed for the job it was then when it hit me. I was sitting in the men's thinking room and thought "Why does it have to be the starter? The EAS also uses the same fuse (makes no sense to me why it is like that but anyway it is what it is and obviously people more in the know made it so it must be right.....ish)."
So after another day of reading and testing the battery and EAS (I can't get under the car at the moment so having tested the starter plus I figured I'd leave that until I have completed these jobs first. Anyway, I discovered that everything was fine when doing a continuity test except for the power to the compressor. The compressor itself is showing 0 and the multimeter gave a little beep as I believe it should do from what I have read and watched (electrics are a dark art to me). It was then when testing the continuity from the connection from the car to the compressor I found it was reading roughly 40ohms and not zero like the others. Anyway, after much more reading, watching videos, and testing it would always give the same reading. Not knowing exactly what I was doing I wanted to make sure I was doing it right. I also tested the connection for the valve block itself and the multimeter beeped as it should do, which made me happy.
So, now having read your post it really got me thinking. Like yourself, I had replaced the air compressor over a year ago now (about November 2019). Just as you did I also bought a compressor off eBay made by Dunlop and it was brand new. But then a few months after having replaced the compressor the new one failed. It just wouldn't work at all. I tested it and no matter what it wouldn't do anything at all. I contacted the seller and he was more than happy to send out a replacement new item, same manufacturer. This was about March of 2020. Since then we have had no issues with it at all, until now (I think). So now I am really wondering if this was the same brand you bought and were having problems with.
Does all of the above appear to be what happened for you? My car is a 2001 4.0HSE.
Thank you in advance for taking the time to read all of the above and if anyone can point me in the right direction it will be greatly appreciated.
Kind regards
Craig.