It's unusual to get a DVR stolen. I think this is the 1st instance I've ever heard of on this forum.
I have a BI pc but I'm going to hide mine in a piece of ventilated furniture and to stop the top from being opened, I'm going to fit magnetic baby locks as these are completely hidden, keyless and yet resist enough to convince someone it's something that doesn't open. Obviously the furniture will be something that hides it inside well so you can't tell there's anything inside unless you start checking for cables at the back. Even then, easily mistaken for some kind of light in the unit. Another way with a pc could be to have it out in the open but fit the type of locks they use in offices to lock it to the ground / desk / wall. If the pc is also silent and has no lights, you could always stick a hand written sign on it saying broken, do not use, espeically if the case looks old. If you have another pc, they'll probably steal that and leave the broken one alone.
An option with your DVR could be to use Network Video Recording so have an external network connected hard drive hidden somewhere other than the house.
You burglary sounds highly unusual to me. I don't know whether you live in a very high end property, but the average burglar, wouldn't turn power off, bypass alarms, etc etc. Most just break a window or unlock a door, rush in, grab what they can see in a quick 10 min walk through then exit. Yours sounds very well planned from some one who may have inside knowleadge of your property or what they were stealing / hoping to steal there.