From the log file I see:
ERROR> –> Unable to move file C:\Program Files\MCEBuddy2x\working0\America’s Got Talent (2006) - S13E25 - The Champions One.mkv to \KICKIT\Media\Tv\Tv(P)\America’s Got Talent (2006)\Season 13
Error :System.UnauthorizedAccessException: Access to the path is denied.
It means that the engine isn’t able to write to the destination folder. I see that you’ve defined a username and password for the network share in your monitor location (as mentioned by @Will_Tschumy), so I’m going to guess that that username doesn’t have write access (it can read) to the destination NAS path.
Keep in mind that this has to be set at two levels, first is the NAS sharing permissions must provide write access to the user and the NAS filesystem (eg NTFS) also must provide write access to the user.
You can also check this topic of other reasons like the NAS time being out of sync with the PC etc.