In this game, the blue side bottom lane tower was not shooting at all. Every other tower in the game worked, just this particular one that was bugged. I'm not sure if it is possible to get a replay of this game or not, but here is the link to the match history page that should give all the information needed.
http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/1984027751/209341270
The same thing just happened to me. Blue side bot tower refused to shoot at any minion or champion that was in range. The only exception was that if we were attacked under the tower it shot the champion, but once the champion was out of range the tower went back to refusing to shoot.
http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/1985149648/49979954?tab=overview
None of the champions are the same across the two games, I can only assume that this bug is completely random. It always seems to be the blue side bottom lane outer turret though.
