[SOLVED!] Feel free to use any of these methods to fix your FPS Spikes!
First Situation I had:
Even though this is my first post, I have read quite a number of other posts relating to FPS Spikes and have yet to find an answer that helps my LoL run.
I have been playing LoL for quite a while and after the Renekton patch, I believe, I started receiving FPS lag in game starting from around 2:00 Minutes in. Whether it's just me on my screen or 5 champs on my screen, my FPS never fails to drop to 2-3 from the previous 30-40. I can also tell you that the major patch recently did not help whatsoever as I did uninstall LoL for a month or 2 before reinstalling it (hoping the newest largest patch would do the trick, but unfortunately did not).
Methods I have tried:
1. Worked with ATI Catalyst Control Center a bit (failed)
2. Shut down my computer and restarted it (failed)
3. Repaired LoL (failed) (RECOMMENDED)
*EDIT 4. Updated Adobe Air (failed) (RECOMMENDED)
5. Completely uninstalled LoL off my computer and then reinstalled it (failed)
6. Downloaded Vista Anti-Lag (Vista Anti-Lag), Game Booster (Game Booster) and Advanced System Care (Advance System Care) (failed) (RECOMMENDED)
*EDIT 7. Turned off all sound (failed) (RECOMMENDED)
8. So I thought it was my computer's problem, so then I restored my whole computer to its factory settings (failed)
9. So given the fact that I restored my whole computer to the point of which being practically brand new or just when I bought it, it still didn't work properly; I uninstalled LoL for around a month or 2 to see if the latest large patch would work (failed)
EDIT* 10. Turned FPS settings to Benchmark (failed)
EDIT* 11. Disabled Nagle's Algorithm (Nagle's Algorithm) (failed)
EDIT* 12. Updated Drivers, Driver Cards and Audio Driver (failed) (RECOMMENDED)
EDIT* 13. Turned off Anti-aliasing and switched Anisotrophic level to x4 (failed) (RECOMMENDED)
EDIT* 14. Updated Graphic Drives AGAIN (failed) (updated DxDiag.txt is shown)
EDIT* 15. Defragmented my computer (failed) (RECOMMENDED)
EDIT* 16. Play LoL on different Internet Connection/Wireless Connection (failed)
EDIT* 17. Turned off Vertical Sync (failed)
EDIT* 18. Uninstalled Pando Media Booster (failed)
EDIT* 19. Downloaded CCleaner (CCleaner) (failed)
EDIT* 20. Run LoL as Admin (failed)
EDIT* 21. Setting LoL priority to high; alone (failed)
EDIT* 22. Setting LoL priority to high; while other running processes are set at low priority (failed)
EDIT* 23. Installed Leatrix Latency Fix (failed)
EDIT* 24. Opened Google Chrome while playing (failed)
EDIT* 25. Installed ACE Client (ACE Client) (failed) (RECOMMENDED)
EDIT* 26. Bought a new, updated Graphics/Video Card and added another Gigabyte of RAM to my computer (SUCCESS) (RECOMMENDED)
*Graphics are always at its lowest: including no shadow, vertical sync, and benchmark/stable FPS settings.
So now I'm completely out of ideas and the forum hasn't given any circumstance like mine (out of the many I have read) or a definite fix. I'm guessing its probably a good idea if I post my dxdiag and other stuff on here but I'm not too sure how to post it (format changed after latest patch and never had previous experience with this, sorry).
I find LoL a wonderful game and I wish to continue playing it without the heavy FPS spikes (so it’s actually playable for me). I thank you for your hard work for providing us with such a fascinating game and I would deeply appreciate if you looked at the problem. If you could tell me what and how to post I will be happy to do so.
And for those who have the same problem as me, feel free to try any of the above methods that I have tried. Some may work for some people and some won't, so you guys have to experiment a little. 
Thank you for your time.
*EDIT *EDIT AGAIN Posted the Dxdiag.txt <---Updated Driver Again to 2010 - failed 
Laptop is too old and can't support these graphics. Used my desktop computer (with everything newly installed) since it is much better!