Please help; can't connect to game sometimes

This has caused me to get leaverbuster two times in just this month. If this continues, I might have to take a break from League, because not only am I wasting my teammates time because they're stuck with a 4v5, but I might also get myself banned from leaving so many games.

The problem is that after we get through champion select, it takes way longer than it should to open the client (ya know, the loading screen). Sometimes it'll just stay black and I have to force close it through task manager, and other times (of how long it takes, by the time I finally open the loading screen, my teammates are in-game) I load to 100%, then it just stays there. Does absolutely nothing. I tried closing and reconnecting 3-4 times and it does the same thing. Doesn't even say I disconnected, it's just stuck at 100%. My internet is just fine too, because I can load webpages (and the fact I wrote this like a couple minutes after it happened again), and while loading it said my ping was 80-90. Is this something to do with my computer? Is there anything I can do to fix it?