Thanks for the info, that's what a good bug report should look like
From your log files I can see that the error was the one with the security certificates of Java which has been fixed with the Minion update.
And after that it just says it starts but does nothing which was the case if you run minion with admin/priviledged rights in the past and tried to install the new version "over the not uninstalled one" I think.
Question:
I see you wrote you uninstalled the old Minion before the update.
Are you really sure you have used the uninstaller of Minion and uninstalled it, the popup showed that asked if you want to keep your configuration or not (and you either choose to keep it which I assume you did not as you say you do not have any Minion.xml file anymore now).
Did you check the point 14 of the troubleshooting guide, about the ipv4 network switch?
If not please try that.
And maybe you already did the following so sorry if that was the case already:
If you try to uninstall it once again, remove all configuration and then check the install folder if all Minion files are gone (else delete them manually too).
Then install the 32bit Windows version to a new chosen folder and allow that in your Antivirus tools.
If that neither helps try to disable the protection of your Bitdefender software in general for 1 try, to see if that fixes it maybe?