Answer: It does sound like you have some sort of fungus at work in your yard. The only ones I can think of that even remotely resemble algae or slime is Pythium Blight.
I'm not sure exactly where you are in the world, your question just says "international". This disease is common in warm, humid weather. High soil pH makes it worse.
You should have your soil tested to make sure the pH isn't off balance. I notice that you have tried aerating the lawn with spiking, you might want to consider having a lawn service aerate with their specialized equipment.
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