[CLIENT] Game sometimes drops to 0 fps and lags my entire laptop

This problem occurs about 20% of the time I play League of Legends. The following will always happen:

Game starts up, lobby is fine, everything is good. People choose their characters, and lock in. Goes to the character portraits, and I have my standard ping (around 80). When the game begins, everything is fine. However, after buying my items and clicking, the game will freeze to 0 fps.

Notes:

1. When this happens, my entire laptop slows down ridiculously. However, when I play a normal game of League of Legends, it's perfectly fine. To illustrate, if I play a normal game of League of Legends, if I press alt+tab it will bring up whatever else I have open relatively fast. No lag at all. However, when the game drops to 0 fps, the mouse is on a 5-10 second delay, and even pressing alt+tab takes forever.

2. If I click a bunch of times with my mouse, there will be the beep from the laptop (usually happens when you're doing something you shouldn't) and then the game stops lagging for a moment, only to begin lagging again.

3. The other players seem to be unaffected but this may not be true.

4. I have seen similar problems occur to other players who play with me sometimes.

The side effects:

I have previously just dealt with it and moved on. However, I was given a 5 minute penalty for 5 games (25 minutes of waiting) because of this. Now it's at 10 minutes (50 minutes of waiting) and I don't really feel like I should wait this long when I didn't even want this to occur, let alone have the punishment become more severe.

The cause:

My assumption is it is due to connection issues with other players. The reason I state this is because it doesn't happen with everyone I play with, only few people - and it isn't character specific either. I have played the computers as well as had teammates with practically every character. Additionally, this lag has happened with characters that I use myself sometimes. My thoughts are that this happens because of people connecting from places they shouldn't be. What I mean by that is that I am in the NA server, but I have played with people from the Philippines. When I did, everyone (including myself) admitted to having a delay in the game (it was like every 0.5 seconds you would move or your action would happen all throughout the entire game).

Conclusion:

I would like for you to revoke these waiting time punishments on my account. I don't play too often, and don't have too much time to wait around to play. I would appreciate it if you could revoke the waiting times on my account, and try to address this issue. More importantly, I believe that maybe the matchmaking system for the matches could be improved upon to reduce such issues.

Game Mode: Co-op v.s Ai, Intermediate, Summoner's Rift Character: Heimerdinger Server: NA