I'm having the same issues. I've tried:
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Reinstalling
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ipconfig release, renew, flushdns
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Turning Firewall off
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Updating Drivers
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Updating Windows
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Configuring DNS
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I have no packet loss
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port forwarding
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made sure there was no VPN or Proxy Usage
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Disabled Internet Protocol Version 6 (TCP/IPv6)
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Synchronized with "time.windows.com"
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Uninstalled all Recording software
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Disabled IPHelper
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Reset computer several times
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Power-cycled my modem/router
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Contacted my ISP
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Added LogitechSupport=0 in Riot Games > League of Legends > Config > game.cfg (open with notepad - under the "[General]" tab) - I do not use Logitech equipment
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Removed Logitech files from Riot Games > League of Legends > RADS > solutions > lol_game_client_sln > releases > 0.0.1.126 > deploy
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Pinged the server <0% loss>
When I log in, it often takes a while to log in and sometimes it gives me an "unable to connect" pop-up window. The client also will log me out of PVP.Net chat and I have to connect manually (sometimes over and over). I cannot spectate any games without crashes (this is 100% of the time). The game goes to a black screen with errors after champion select for the most part. Sometimes it runs flawlessly. But nine times out of ten, I'm looking at 3-4 "ALT - F4" > Reconnect before I can get into a game.
TL;DR - I did a bunch of stuff to fix it, didn't work. What I tried might work for you.