Answer: If the drainage is poor then the soil is probably very compacted, and/or infertile, and/or very acidic. You will need to correct this in order to get grass to grow and to stop the mold or algae or moss. Also, keep in mind that grass needs full sun and relatively good soil in order to grow and stay healthy.
You might start by looking at how water drains on your property to try to divert runoff away from that area to prevent it being inundated during rain storms.
You need to run some basic soil tests to check fertility and pH to see if you need to lime (lime will make soil less acidic). Use the test results to determine how much of each is needed.
Then you would want to loosen the soil by using a core aerator. This tool can be rented; it pulls up plugs or cores of soil and leaves holes in the ground.
Then you would top dress with compost to provide organic matter for the soil to help it hold air.
Your local county extension should be able to help you with the soil tests and interpreting the results. They may also have suggestions on how to prevent the mold. Good luck with your lawn!
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