I believe I've found a piece to the puzzle.
The same thing happened to me around two weeks ago -- the countdown to the game got to 0, and the client came up with "Game is still in progress...". Oddly enough, I could hear my teammates through League Voice, and they were in the game. For whatever reason, I was not. Mind you, this was also after I downloaded and installed Patch 9.9.
So I reported the bug and started looking things up. This was the most recent thread on this subject that I've come across, hence why I'm posting the solution here. (For reference for the following explanation, I'm using Windows 10.)
I was considering uninstalling and reinstalling. I at least went to kill the game in Task Manager by going to Apps > League of Legends (32 bit), clicking the dropdown arrow, right-clicking on one of the instances of League, and clicking on "Go to details". I was taken to the Details tab and had right-clicked on one of the instances there. I was about to click "End process tree" when I noticed something odd:
There's a column called UAC virtualization, UAC standing for "User Account Controls". In that column, one instance (which I imagine was the instance of the game itself), UAC virtualization was listed as "Enabled". All other instances (which appeared to be tied to the game client) were listed as "Disabled". I'm still trying to grasp what all of it means, but the keyword that stuck out to me was "security".
My first thought was Windows Defender Firewall. Whenever a patch is done, a Firewall popup window comes up, asking what networks to allow League to operate on/through. So I went to Control Panel > System and Security > Windows Defender Firewall. On the sidebar, I clicked on "Allow an app or feature through Windows Defender Firewall" and scrolled to all of the instances of League of Legends. Sure enough, one of the instances was not allowing League to communicate through private networks. I was at home and plugged into my router by ethernet (which I think automatically counts as a private network). So what I did was click on the "Change settings..." button, click the checkbox under the "Private" column, and click "Okay". I also checked my Wi-Fi Settings, and my home connection had somehow changed to Public, so I changed it back to Private.
After that, I killed the game in Task Manager how I was going to above, reopened League, and logged in. Lo and behold, it took me straight into the game. Unfortunately, that took so long that I was deemed a "Leaver" for that game and was given a Leaverbuster warning. (Not gonna lie, I'm not happy about that, considering I never go AFK and I sent them a bug report, but it's whatever.) The only reason I got one, though, is because I was troubleshooting. If you know about the fix beforehand, you shouldn't run into this problem. (My roommate had the exact same issue and I guided them through the fix. It worked, and no Leaverbuster warning was given.)
Hope this helps!