My answer when this situation came up was to attach the TV to the wall and get an HP Microserver, all set up as a media centre. I've tucked it away where it can't be reached easily and the TV is attached to the ceiling (a wall would do.)
Even if they can reach it since it's a server it's just a black box and doesn't have any interesting lights to speak of - that means the little monsters don't have any interest in it. Everything is ducted in (not that there's much anyway.)
The only accessible point is the power button, which is disabled so to power the machine off you either have to go through the software or hold for 10 seconds. Even opening the drive tray is done via software.
I've copied all our media onto it and got rid of all the other boxes. As a bonus it also shares out media that I can pick up from phones, or raspberry pi's set up as adapters for the rest of the house. All the other boxes (set top box, games console, dvd and the like) are gone which makes cabling a lot less fuss. If you wanted to a box like a raspberry pi can be put in behind the main TV and even have the server elsewhere.
The biggest risk now is a toy hitting the screen, juice in the wireless keyboard or biscuits in the Blu-ray drive and none of that is a big deal.
All in it probably cost about the same as a decent Blu-ray player but is a bazillion times more flexible.