I've had this problem for a while now too, and no replacing LocalConfig.xml or Patcher would fix it for me
Eventually I got it going with a timing thing. It seemed that the PatcherSetup.exe was botching the LocalConfig.xml whenever it ran and causing a Hash conflict, so instead I ran ConanPatcher.exe so that it would have it's usual Hash conflict (usually I would let that complete and then the patcher would auto-run and screw the .xml again and re-run the launcher to no avail), but this time I stopped the first launcher and closed it before the bar loaded and then checked the "Patch.log" file.
(NOTE: I copied in an old copy of a LocalConfig.xml file before doing the above)
In there you can see the hash number that's from your original LocalConfig.xml file because the PatcherSetup hasn't overwritten the .xml file yet. You can also see what hash number the launcher is expecting to see when it's trying to run the launcher properly. I copied the number that it was expecting to find into my LocalConfig.xml file and it worked. This is after trying numerous different xml files, re-installing completely, trying copied patchers, none of the regular fixes seemed to work.
(quick steps that I did in case there's anyone else with a similar issue)
1. Copy in a LocalConfig.xml file to your Conan folder - I used this one and saved it as a file on my desktop, then I could copy it in when trying different fixes:
I used US Version
2. Run ConanPatcher.exe and stop then close the launcher before the bar finishes loading
3. Open Patch.log and open your LocalConfig.xml file (the one inside your Conan folder)
4. In your LocalConfig.xml file is the "<PatchVersion>" hash number. In this example, mine was x01d6f8f8ffd146eab449b2dd98ff6fcf
5. Look for that number in your Patch.log file. Mine was the line "PatchVersions are different (
x01d6f8f8ffd146eab449b2dd98ff6fcf != xdbd476510b045d2e2efb7b3e9a050470)"
6. The != means not equal to, so it's showing you what hash number the Patcher wants to see in your .xml file. I know the xdbd.. number is in .xml files available online, but for some reason they still didn't work for me. It was only when I tried the timing thing.
7. So copy the number that the Patcher is expecting to see and paste it into your LocalConfig.xml file. In my example, I copied xdbd476510b045d2e2efb7b3e9a050470 into the .xml, then saved and closed it.
8. Close the Patch.log
9. Run ConanPatcher.exe again. It worked that time.
Again, I'd used the xdbd476510b045d2e2efb7b3e9a050470 number in LocalConfig.xml files before, in many of the frustrating times trying to get it working, but still had the same error no matter which one I tried.
Hope that helps anyone else stuck on the same issue!