Dead grass will not grow back. The only way to repair your lawn is to plant seed in the grass patches. It is essential when planting grass seed to properly prepare the ground. Seed will not germinate unless it is in direct contact with soil. Hard, packed soil full of debris is not a good base for new lawn. The soil needs to be loosened up and fertilized.
Remove debris from the area you want to reseed. Use a rototiller to break up and loosen the top 4 to 6 inches of soil. Pull out any existing grass and weeds.
Add 1 inch of sand and 1 inch of compost to the patches. This will add nutrients and improve water drainage. Rototill both into the top inch of soil.
Apply a starter fertilizer high in phosphorus. Read the packaging to determine the rate to set the broadcast spreader.
Spread grass seed with a hand spreader. If you are reseeding a very large patch, you can use a mechanical spreader.
Run the back of a rake on top of the grass seed. Mix the seed into the top of the soil mixture.
Set a sprinkler to the oscillating setting. Water the grass patches for 5 to 10 minutes twice or three times a day. Continue this watering schedule for the first 10 days. Once you notice the seed begin to germinate, cut down on watering to once daily for 15 to 30 minutes.