I'm having very similar issues consistently on both Live servers (NA) and PBE servers. Upon attempting to load in game, just after champion select, the loading screen never appears anywhere but in my task bar. If I try to click on the task bar icon, I'm given a critical error -
https://prnt.sc/pm1gtv
Which leads me to-
https://prnt.sc/pm1gwb
I'll then generate the dump, etc and copy it to clipboard just in case (Though I do believe I just accidentally lost it by copying those screenshot links, whoops, I'm an idiot...)
The only thing that's helped it, at least temporarily, is restarting my entire system... which just isn't a feasible "fix" when my laptop takes ten years to reboot, and every second in a match counts PLUS it's only temporary, and the error can happen again at any time...
This just happened to me on NA about 15 minutes ago, and my team did a remake.... I wear to God, if I end up with leaver penalties because of this I'm going to be REAL upset. I take my account and reports/penalties very seriously - I almost never leave a game, even if I'm about to pee myself, I'm that worried about negative marks on my account.
I'll try the solution that "markichi" posted... fingers crossed.