So we actually can watch your replays. I didn't see anything wrong in the Eve game. In the Warwick game the only thing you did was "not help kill the enemy team while they were wrecking your base." However, I don't think you could have done anything. But it looks pretty bad, since when the nexus blows up you're pushing minions in a lane that doesn't even have an inhibitor down....
https://i.imgur.com/sQcUDqn.png/img
https://i.imgur.com/YaH1YyU.png/img
https://i.imgur.com/eZq7duM.png/img
https://i.imgur.com/EyPRzsY.png/img
#HOWEVER
The Kayne game. You are counterjungling while super behind, and then appear to.... Attempt to proxy farm your mid laners caster minions and then die (you are level 4, enemy mid laner is level 6 and almost full hp - and you take one turret shot)
Screenshots of this death
https://i.imgur.com/7N1ZVfL.png/img
https://i.imgur.com/wXamNBL.png/img
https://i.imgur.com/44Bs2iU.png/img
https://i.imgur.com/XIue8LY.png/img
https://i.imgur.com/d21EAEe.png/img
And then.... Your next intentional death. You walk up to the level 6 enemy bottom laners, alone, while level 4, while outside of your turret's protection.... To.... Defend the turret? To die and attempt to kill some caster minions? lol
https://i.imgur.com/ZNZOmFY.png/img
https://i.imgur.com/KXnhyzM.png/img
https://i.imgur.com/nXSyFqr.png/img
And then your next intentional (sort of?) death. You, being super duper behind, attempt to duel the full health level 7 Ornn (almost level 8 - reaches level 8 by the time you die) when you have just reached level 6 and have no gold or items.
https://i.imgur.com/LnuPZt8.png/img
https://i.imgur.com/wxDTY5g.png/img
https://i.imgur.com/FOqET3p.png/img
https://i.imgur.com/BZGP85x.png/img
https://i.imgur.com/Kp6pRhs.png/img
You do, however, appear to play normal after that. Just farming and taking dragons. I don't know what you said in chat. But it looks like you had 3 intentional deaths in one game (with only one of them being questionable - so 2 ints for sure). Does this deserve a 2 week ban? Well I didn't see the chat. I don't think 2 intentional deaths deserves a ban (especially since you won the game), but... Don't try to play it off as innocent. You did int. You just didn't int hard (and it was only in one game, not 3).
If you were banned JUST for these games, I honestly think you deserve a chat restriction instead. If everyone who griefed "just a little bit" got hit with a 2 week ban, I think 10% of the League population would get hit. Heck I had a game today where I said "im afk" and AFKed for 10 seconds (in response to a teammate griefing me and pretending to help me with dragon then leaving to let me die). Do I deserve a 2 week ban for AFKing for 10 seconds? I'd hope not. Does the guy who left me to die at dragon deserve a 2 week ban for letting me die? If that was the only game he did it, no. (Note: The guy who left me to die at dragon griefed in another way as well - he initiated a surrender vote as we were winning. 3 people total voted yes. I was really mad at him, and really wanted to vote yes, but for the sake of the one person who actually wanted to win, I did not vote and it failed 3-0, and we won like 30 seconds later)