You will want to kill off what is there with a Round-Up type product. Otherwise, you will see virtually no results. With the weed killer treatment, however, you can see some nice results without any heavy equipment. After all dies off, you should rake off the excess dead matter and also rough up the surface a bit, then seed it and press in the seed if you can, if nothing else using your boots. Some lime, as mentioned, probably would help too. You can get a Round-Up type product (glyphosate) very cheap at an agriculture supply store or online at about 1/8 the price of what you would pay typically at a home store for "Round Up".