Move to the folder:
League of Legends/Config/
Delete the file 'game.cfg' and 'input.txt'
Relaunch the game, try to spectate someone.
IF that still doesn't work, move to these two folders:
League of Legends/RADS/projects/lol_game_client and lol_game_client_en_us
Delete both of them.
Then run the repair option in the launcher, by clicking the cogwheel in the upper right hand corner.
League of Legends/Config/
Delete the file 'game.cfg' and 'input.txt'
Relaunch the game, try to spectate someone.
IF that still doesn't work, move to these two folders:
League of Legends/RADS/projects/lol_game_client and lol_game_client_en_us
Delete both of them.
Then run the repair option in the launcher, by clicking the cogwheel in the upper right hand corner.