lol. first thing to notice " mitsubishi mirage PUSH START" 2ndly when you tried to start the car, "first brake felt tight and when you started the car, a bird found dead under the car" yes cuz that is what normally we do, we start the car and if it dosnt start, we look UNDER THE CAR instead of under the hood
ok on a serious note, it is possible that the bird somehow went inside the engine bay and became a prey when the car started. maybe it got mangled in alternator belt or something. anyway if the car is now running fine, you should be ok.