I guess my toaster no longer accepts the new summoner's rift. (Rioters needed)

Ever since the update of the new Summoner's Rift, I have been experiencing a massive losing streak. These losses were mostly not caused by my mechanics or so--although it may look like it--but it was truly my FPS that prevented me from engaging in any FPS-intensive team fights. I am now too afraid to play any ranked games, even normal games, because I cannot win anything. Not just teamfights, CSing became a huge problem, too. I've also tried many things to boost my FPS but none of them actually worked. Any Rioters that can help me resolve this is truly appreciated.

(NOTE:

1. This computer CANNOT be altered due to personal reasons, so don't tell me to get a new computer or graphic card, etc.
2. FPS did not increase but rather decreased by 5-10.
3. Average FPS per game: 30 when left alone, 20 when CSing, 15 when ganked, 5~10 when teamfighting
4. When entering the new summoner's rift, sometimes the textures turn blue and forces you to relog.)