[CRASH] Game does not launch after champion select

After champion select, the game will not launch, no matter how long I wait. I must log in again and try to reconnect.

1. Play a game, it does not matter what mode.
2. Finish Champion Select.
3. The League Of Legends splash does not appear, even after a minute.
4. In the tray, click on the Riot Games icon. It brings up a window saying that the game is still launching.

In order to connect to the game, I must:

1. Quit the client and relaunch it.
2. Log in.
3. It will say "Your game has disconnected. Please reconnect."
4. Press the Reconnect button. Most of the time, it will not reconnect even after waiting a minute.
5. Repeat steps 1-4 as necessary.

Half of the time I am able to join during the loading screen. The other half of the time, I join at the 2nd to 5th minute mark, which already sets me back several CS. One time though, I joined at the 10 minute mark IN A RANKED GAME and was reported for AFK at the end. Now I have to unfairly suffer 5 games of low priority queue. I have repaired the client and reinstalled it. This bug still exists on my computer, and has existed since patch 5.7.

My computer specs are as follows:

• Intel i5-4460
• Radeon R9 270 GPU
• 8GB RAM