Chat logs if you want to know_ exactly_ why you got punished.
As for the normals things. Absolutely nothing wrong with "try harding" in norms- just understand this fundamental difference- the people that play ranked primarily view normals different, and the people that play normals primarily view normals different.
Normals are "always" a serious game to, probably 90-95% of the mostly-normal playing population. That may be confusing but read that a few times. Whereas Normals are a way to "kick-back", experiment, try new champs, and "have fun" for the 90-95% mostly-ranked population. Thats not to say that people that play ranked don't also take normals seriously- just a lot less of them do. Same goes for the people that play ranked. Convoluted, but it really makes sense and boils down to this:
The game-mode you play the most is going to be what you take personally serious. Thats why you get people sometimes raging about ARAMS and having unbalanced runes, or OP champs, or rerolls being OP/weak, or that they should be able to ban certain champs. The people that play that almost solely take it way more serious than a casual that plays less than 2% of his games as ARAM. Hope that makes sense.