A broody will stay on the nest for a day or even two, I haven't always given them food, just some water and most times they get off the nest sooner. Your hen seems to sleep more than usual by the way you are describing her, so I would continue with the water, just hold the bowl to her and take...
I hold a small bowl of water to the broody when she's on lock down and again during and just after hatch, if she hasnt come off the nest with the chicks after 24 hours I'll set a small dish of wet chick feed next to her in the nest. If she poos in the nest box I'll reach in with a paper towel...