Thatch builds up where there is not an active Soil Food Web to digest it. That the soil stays too wet too long tells us that there is a drainage issue.
Start with a good reliable soil test, UMASS does that for pH and major nutrients, then these simple soil tests may be of some help,
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell, to9 a point. Too much organic matter can be bad as well.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

From the information provided the soil needs much more organic matter and few "fertilizers" will provide enough. Without addressing, and correcting, the soil issues the lawn will not do well. Also shade appears to be an issue so grasses more tolerant of shade may be needed.

Here is a link that might be useful: UMASS CES

Please see my post with the same "Subject of Posting" tittle on the Lawn Care blog.
I have provided pictures of my lawn and a little more details.

Please provide an opinion and your thoughts.

Thank You

Front Lawn

Front Lawn Close Uo

Front Lawn Rakings

Back yard lawn

back yard close up

Thatch layer

There are 2 different ideas of thatch in grassy lawns.

The dead grass blades that cover the soil between plants is not a serious thatch issue.

The other thatch issue involve the roots and stems growing above the soil simply feeding on the water and fertilizers as they are applied. The problem with this type pf thatch is more severe because there is very little root growing into the actual soil.

Your last photo just has some grass and a dark spot on my screen, so a caption of what we are looking at would clarify which type of thatch you are concerned with.

There is a lot of misunderstanding of what lawn thatch is. Lawn thatch is not the accumulated grass clippings, lawn thatch is the accumulated dead grass plants. Lawn thatch accumulates because the Soil Food Web is not active enough to digest it.
Some lawn thatch (about 1/2 inch) is good, too much can be a problem. To keep lawn thatch under control you need to encourage the Soil Food Web which means maintaining adequate levels of organic matter in the soil.

Dead plants make up the simple thatch that most people think of when they want to dethatch their lawns.
The serious thatch is made up of living and dead stems and even living roots that have been living on top of the soil.

I agree with kimmsr on the lack of food web activity because most of the time the only place roots get enough air, water and fertilizer is when it is applied to the surface.

This is the type of thatch that created the need for aerators.

Thatch did not create the need for aerators, compacted soils (soils lacking adequate amounts of organic matter) created that need.