LoL seems to freeze every time anything significant happens...help me please :'(

Hi Summoners, I've been dealing with this issue for a while now and have just been dealing with it regardless of the rage and tilt it can cause at times, but I finally decided enough is enough and wanted to reach out for help. The problem: When I'm in game and someone dies (anywhere) on the map and the notification is announced that someone has been slain my (entire) screen freezes including the sound too a lot of times. Or, when dragon or baron has been slain it freezes. Last but not least when i get ganked by anyone that comes in lane my game freezes. When i say freeze, i don't mean lag or a short freeze. I mean a freeze that normally last over 5 seconds. Sometimes even up to 20 seconds or so if a lot of chaos is going on. I'll add quickly that the client in champ select does it often as well and got me in low priority a few times as well as lost me so much LP. Is this a computer issue? If so, would a better graphics card do the most good, or a new cpu? It's an Intel i3 cpu and i believe it's running on the graphics built in to the cpu. Or is this a game issue? Please help me conquer the solution :)