So this is gonna sound downright crazy, but it just popped into my head and is too funny to leave out ....
First, I suspect that years of poisoning the "weeds" and taking the clippings off of the lawn and watering too frequently and mowing too short has slowly turned your soil into cement-like dirt. Although the sod in your picture does have pretty good color!
But the fact that you cannot dig much deeper than six inches tells the whole story.
And so it makes me think: what this woman really needs is some kind of plant that has a massive tap root that will punch deep into the soil and open up channels so that the lawn can then go deeper ..... something that will really rip up that deeper soil ....
And here is the funny part: .... like a dandelion.
Okay, so you aren't going to intentionally plant dandelions in your yard.
I would like to hear about worm discoveries too.
It is normal for your grass to not grow much in the summer.
I suggest that you wait until the first of september and then put down some fertilizer and really go to town on mowing high. The grass will eventually send down deeper roots and start to break up that cement-like dirt a little.
If you are impatient and want some proof, that there is truth to all of this, dig a hole two feet deep and then refill the hole with a mix of sticks, leaves, kitchen scraps and dirt - leave it mounded in your yard and then notice how this fall it will fill in with grass and next spring it will be the thickest, lushest turf in your whole lawn.