[CRASH] About 50% of the time, loading into game crashes my internet

After champion select, no matter which mode, at the loading screen to get into the game my internet will crash, requiring me to restart my router to get into game. After the restart, even if my internet is working, if the game hasn't started yet (i.e. someone still loading) then I get kicked off again and have to repeat the process. This happens to me randomly throughout the day, and though I feel it's more often than 50% of the time, I also know that I'm paying more attention to the times it doesn't work. I have revalidated my League files using the patcher, but this has not fixed the problem.

1. I join a queue (any game mode)
2. After champion select, the loading screen pops up and I begin to load into the game
3. [BUG] At a random point in the loading process (the percentage I am loaded differs from game to game) my internet will drop out and the game will tell me I have disconnected. It will also kill any open connections I have at the time, such as Skype or Steam chat.
4. I restart my router and hope everyone is in game by the time my router finishes rebooting
5. Attempt to reconnect
6. Repeat 4-5 until I get in game

If anyone knows of a fix for this, please tell me. Also of note (possibly) is the fact that my internet will not connect for the first few minutes my computer is on. I have tried reinstalling my network adapter driver, but that did not change the problem.