hello simsan,
From your description, there is a short circuit in the starting circuits. They have their beginning in the keyboard ... hence the conclusion. Based on my experience with macbook repairs, the computer has been flooded (maybe it's just condensation under the keyboard due to working in certain conditions, maybe something else). Usually this means that something spilled on the keyboard some time ago, was worn off and a few weeks or even months have passed ... However, corrosion, like tooth decay, is inevitable :-)
You need to open your computer and take a look at it. Perhaps it's nothing terrible and expensive. Unfortunately, time plays against you.