Help me diagnose my lawn catastrophe!

[gaignum]

Let me start from the beginning. I live in a townhouse in NC and have for over 3 years now. The first 2 years I lived there I would allow my dog into my backyard to use the bathroom. You can imagine what my 600 sq ft backyard looked like after being urinated on for 2 years. The grass was dead everywhere, and as a result water would tend to pool in my backyard causing some type of mold. I worked with a landscaping crew when I was younger and do my research through and through, so I thought I would have no problems.

In May of this year I did all the preperation and resodded my back yard. I pulled up all the old grass, used a tiller to soften the ground several times, fertilized, used a lawn roller to even and make sure the sod was tight. I even bought a sprinkler timer to be sure that the grass was properly watered every day. I watered religiously for 6 weeks until I could feel the sod firmly attached to the ground when I tried to fold it up. The grass was a lush dark green and it looked beautiful.

Now lets fast forward 2 months in the future to now.
[img]https://i51.tinypic.com/1rwvnr.jpg[/img]

My grass is brown and dead in many areas but not everywhere.
[img]https://i53.tinypic.com/2iltme.jpg[/img]
Before you even ask the dog has not been allowed into the backyard since I layed the sod, so it is not pet related. Water is definitely pooling a bit around these dead areas. And there is a black mold forming again in one area where it is particularly barren.
[img]https://i56.tinypic.com/xmmq03.jpg[/img]

So now I need help with the diagnosis/solution to my problem. Since the grass isn't dead everywhere and ironicly enough seems to be dead in the areas water is forming I'm assuming the ground is not level in these areas.

If this is the case, I saw that many people were leveling these areas with a topsoil/sand mix and allowing to to settle and then reapplying to even. I would then lay down some grass seed to try to solve the issues. Do I need to remove the dead grass before I do this or can I just lay the dirt over it?

Of course I may be entirely wrong, which is why I'm here. Please help!