The BuyButton is associated with purchases of MC, but you could be right. It may also get invoked when you reinstall and/or apply the licence again.
I used to be able to lock up the Server pretty easily when I was doing a lot of testing and mucking around on the Client. Doing stuff like View modifications on the Client (which don't get synced to the Server), changing Libraries often, generally testing bits of functionality. But I haven't locked up the Server for some time now. Maybe coincidence, maybe not. So if you have been doing lots of testing, rather than just playing audio, that could be a cause. MC, or the Client/Server part of it, seems to sometimes get a bit out of whack, leaving the Server in a hung situation. I have even completely crashed the Server with some of the stuff I do. But I can't define what exactly caused it, because it could have been lots of things.
Aside from that, your logs still looked like a network issue.
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Try this. On one of the PCs open a Command Window in Windows. The run the ping command continuously against the other PC for some time. You shouldn't see any dropped packets. The ping command to use would be;
ping -t <the other PC IP Address>
Help for ping using command. Note the use of Ctrl+Break and Ctrl+C;
ping /?
I get less than 1ms response time on my wired network, as should you.
If you don't get any lost packets in five minutes, reverse the process so you ping from the other PC back to the first you tried on.
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There is a lot of DLNA broadcast activity on your Server, which is normal. But if you don't connect to the Server using DLNA, or push media to a DLNA Renderer, you could turn off the DLNA functions in Media Network. Of course leave Media Network running, and continue to use the Access Key method to connect.
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I can't see in any of the logs that you are actually playing, or starting to play, any file. What is the full path to the audio files you were playing when the Server crashed? Just the base path if you don't know the file being played. I'm not sure the logs actually caught the crash. There is no Crash Dump in the zip, which there usually would be for the Server. The network errors I'm seeing are just URL, HTTP, and Socket errors, not file errors.
Well, there are a bunch of Sharing Plugins Read failures. If you have additional, non-default plugins installed on the Server, perhaps remove them and see if the problem goes away.
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Other than that, perhaps capture a new set of logs when it happens next time, and note the full path and filename that the Client was trying to play. It should be visible on the Client, since it hasn't crashed.