My client and my PBE isn't opening on my computer or my laptop. Can someone help me fix this problem? On my Mac it says my startup disk is full but I already cleared 15 GB and it's still not opening. It keeps crashing before it even gets to 35% complete of downloading. Please help I don't know how to fix this problem. 
Me too though idek damn
Try to click on the link, and click what kind of computer you have.
https://support.riotgames.com/hc/en-us/articles/202539040-Reinstalling-League-of-Legends
Afterwards, do it and see if it works. If not, you need to send them a support ticket and tell them what the issue is in a more in-depth analysis.
http://support.leagueoflegends.com/
Edit: I found similar things here that might help.
https://support.riotgames.com/hc/en-us/articles/201761944-Login-Issues
https://support.riotgames.com/hc/en-us/articles/201752664-Troubleshooting-Connection-Issues
Edit (2): Hey, if I may ask, if it's stuck anywhere between 30-40%, are you getting "files being scanned"? This has also happen to me, and it had about 3000-4000 files to scan. I waited like 30-40 minutes, depending on multiple factors; afterwards it started up for me and I didn't have the problem. Try to wait, if it does not work, support is your best bet.
