Periodic blue screen

From your description, I would say you need to clean the cable connections.

My guess is that the Samsung will show a blue screen if it does not sense an incoming video signal -- the blue screen would be a default display when there is no signal.

I would start by checking the video link. Try replacing the cable between the Jaton and the Samsung. If this doesn't work, see if the video cable sockets on the Jaton or the Samsung are loose or damaged. You mentioned the cables "brought the plug 'housing' with them." I'm not sure what this means, but it suggests that maybe something might not be right at the sockets of at least one of the components.

If the link seems OK, then something more serious could be going wrong either in the Jaton's video output circuitry or the Samsung's video input circuitry. Replacing one of these two with a good working alternate (do you have another TV? maybe a computer screen?) would help identify which one is faulty. The hard part is that your problem is only intermittent at a low rate of recurrence. Good luck.