Can't connect to games [Loadscreen]

Multiple times I have had an issue where during a load screen for Summoner's Rift (edit: also just happened with ARAM) I will load up to 100% and then nothing happens and at that time the ping circle spinner also stops spinning. I can wait for 5 or more minutes and nothing happens. Even more joyful, I cannot minimize out of it (Windows 10). I can alt+tab but get nothing, and then hit the Windows key and see the start menu and task bar. If I highlight and try to close the League of Legends window it does nothing. Ultimately, my only solution has been to manually restart my PC, which then shafts my team. I can reboot and eventually load into the game (dooming my team as they've been 4 v 5 a long time) or not connect and eat the LP loss in ranked with a remake (which is what I do in ranked, because don't want to punish them). I am, as I write this, eating LP loss after staying away from Ranked for a month or two and submitting previous bugs via the bug icon in the client.

I'm not sure how often it happens, maybe once or twice a week, but I play infrequently.