For those of you who are stuck at the logo forever after patch 8.21...
I had this too for about three days and I know, it was frustrating, doing every possible thing to maybe solve this issue. But no, literally all you need to do is this:
Go to:** C drive > Users > (username) > Documents > League of Legends, and then delete the entire League of Legends folder. > Close this window, then launch LoL as administrator just to be sure (right click your LoL shortcut and click "Run as administrator"). **
**However, deleting the League of Legends folder will also delete your highlights/replays (which are stored in this folder). But, if you would like to keep your highlights/replays, just move the entire League of Legends folder to a different location like your desktop. This will have the same effect as deleting it. **
And that's it! No hextech repair tool or deleting all this lol_cache and all that jazz (I had to do stuff like that, but no help). I had to spend hours just reading through all these threads only to get nowhere, but this took me about a few second and voila! I'm back on the rift, just like that.