If you didn't insure it through postal service a claim won't do you much good, I would immediately return it to the e-bay seller and report it as a negative feedback to the seller, there's no way that damage like that could be caused during shipping if there is no debris in the package.
Powering the motherboard is at your own risk, I doubt it could cause a fire or anything more likely it will just cause it to not work properly but I wouldn't trust a motherboard that's had this kind of damage done to it there's no telling what the traces in that area do because again motherboard are many layered devices, considering it's near the edge it might work, but then again it might not. Plug it in and try if you want but I wouldn't keep something like that.