You should see a dam scratching around while her chicks are following her and trying to get underneath her. The chicks get in the way, but the dam doesn't stop kicking at the ground and therefore her chicks get kicked and go rolling around. Chicks are tough under certain circumstances.
Cardboard is one of the most unsafe materials to suggest when you are using a heat lamp, which could easily catch cardboard on fire and kill both you and your chicks.
I am so sorry for your loss! Do you have a brooder that you can put them in? A heat plate would be preferable over a heat lamp if you have one, as they are safer, they do not have a light that flickers (chickens see in slow motion), and chicks that are raised by a dam will be more comforted by...