Then try the other accounts as well. Make sure that none of them appears as “logged in” except the one under which the Plex server shall run.
There is a registry setting, which prevents Windows from starting up the last-used user account upon boot-up (yes, even before the password of that user has been typed in).
This will ensure that Plex server will only start up after you have logged in to the right user account. See Plex now available without logon - #11 by OttoKerner