Update: So I've tried reinstalling LoL, and now the same thing keeps happening (client crashes and my computer goes dark) about 1 minute into the reinstall process.... I have no idea how to get around this. I've hard reset my computer multiple times now and tried again and again, but to avail.
Update 2: I tried adding the certificates, but this hasn't solved the problem either.
**FIXED ** (partially) Update: Ok so I can play league now. I'm still getting the pop up of SSL certificate invalid, but my computer is no longer shutting off during the game, and it made it through the reinstall (which has gotten much quicker than compared to how long I remember it taking). Now this is what worked for me, maybe it's only one of these things that fixed it, but here is the procedures I took.
1: PROBLEM: League was crashing, and in turn, shut down my computer right at minion spawn. Sometimes, I was able to reboot the comp, and get back into my game, and sometimes I was unable. Mind you, I'm playing on a MAC.
First, I tried repairing the client, didn't work. Next I tried reinstalling the game, and then the same problem kept happing during the installation process (computer would shut down).
2: I went to that digicert site and downloaded the 2 certificates that everyone with this problem was recommending -- The High Assurance CA-3 and the Secure Server CA. I downloaded these onto my computer. I went to try and play, but kept having the same issue.
3: I went into the application on the MacOS called "Keychain" (this is where you can change settings on certificates like the 2 that I downloaded). Now when these certs were downloaded, I kept the default settings for these certs. I went into these 2 certs' properties and instead of keeping them on the default setting, I changed them to "Always Trust."
4: BOOM, leauge downloaded and I went into custom games and was able to play through the entire game with no problems. I am still getting the SSL certificate pop up, but I just hit cancel and have had no problems.
Hopefully this helps anyone with this same issue.