Camera works with battery grip but not without it?

The thing with genuine batteries is that they have a charge controller inside them that helps to safely turn off camera if such need occurs. If non-genuine batteries aren’t really cheap and from reputable brand, then it shouldn’t be really much of a problem. If they are, than it might be that camera doesn’t get enough current to start.

A million dollar question is: Does 80D launch with original battery?

If not, that it seems like your battery grip could break something inside of its battery section. After all, chinese guys didn’t adapt their grips for 70D to be usable with 80D, since LP-E6N and LP-E6 are “officially interchangeable” (even though LP-E6N is similar to LP-E6 in terms of looks and shape, there were minor design changes to LP-E6N under the hood, that could do something to your camera, imo).