Answer: This is a very difficult planting site, whatever you do is going to have to be a bit of an experiment. There is an interface problem with the paving under the soil in that it will not drain out excess rainwater so at times the soil will become saturated. And yet, the shallower the soil, the faster the area will dry out during dry spells. Overall this is a bit like planting in a giant container, with tightly restricted area for the roots and no drainage hole in the bottom.
I can't tell you if the grass froze out, drowned, or died of drought, but all three are possible scenarios with such shallow soil. You might want to try to improve the soil with amendments such as compost or other organic material and raise the soil level, and break holes in the concrete to allow excess water to escape. However, this would ruin the concrete paving area for future use as parking or paved area, and it would be expensive, and it would potentially change the grading around the foundation of the building which can cause problems.
You could try re-leveling the soil, and plant grass seed as that is a minimal investment. Plan on watering the "lawn" regularly during the growing season -- not overwatering, but keeping the top six inches of soil damp like a wrung out sponge. You will have to dig into the soil to see if/when you need to water, then water slowly, then wait a few hours and dig down to see how far the water went. Eventually you will develop a sense of when to water and for how long each time.
For your flowers, I would suggest you use large sized containers such as half whiskey barrel sized planters and plant annuals, I would avoid planting in the ground as the flowers will be affected by the poor soil conditions just as the grass is.
Your local county extension may have some additional suggestions based on a better understanding of the actual site. Best of luck with your project!
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