When I tried to uninstall PHNL it asked me if I wanted to remove COUTL as well and I said yes but it gave an error message saying that it was unable to.
This might also due to the fact that the Couatl.exe was still closing, because you might have launched the unstaller too soon after FSX closed down and, depending on your system speed, it might take some additional time before it also close the additional programs ( like Couatl.exe ) that are launched by it.
A Windows reboot would surely have fixed this.
Well anyway, I tried installing the Addon Manager and this time it ended with an error saying the bracket was not closed or something like that. I take some xml was not written properly.
error on line 0,position 0: The following tag were not closed Simbase.Document
This means there's an error in your EXE.XML file (or it's DLL.XML ?), that of course is preventing everything to run. This might have been appeared when you edited to disable the Couatl exe. In any case, it should be possible to manually fix your XML file, by closing the missing ending tag.
OR, if you are not sure about how to fix it, if you simply remove it and run PHNL installer again, a new correct one will be remade from scratch.