This is why you were banned.
Let's review shall we? OP picks Garen. Purchases ONLY boots, no potions, no wards, just boots. Proceeds to die to the enemy adc at 1:34. Dies to the enemy mid just after the 2 minute mark. Dies to the enemy top at around the 3:45 mark. Then appears to go afk. That is not a disconnection, that is not a leaverbuster penalty. What you were doing was intentionally feeding the enemy team. There are many more cases of behavior like this in your match history, but I cannot be bothered to link and describe them.
You were punished for griefing. The system mistakenly classed your punishment as a chat violation instead. Probably a glitch in the system.
My question to you - Why go through all the effort to make this post and try to play innocent? You know damn well why you were banned. Did you not realize that posting this and garnering as much support as you have would result in people actually digging into your account history? You need to be honest with yourself, and with everyone here about why you got banned. Take ownership for your behavior and start taking steps to change it.
edit: or just delete everything lmao. I can understand that people get toxic from time to time. What I don't get is the dishonesty. This was never going to work. You couldn't have realistically expected it to. Just be a man and own up to your shortcomings.