LoL stuck on authenticating (IP problem.. I think)

Hey peeeeps, I'm calling out to the few IT beasts out there. I've encountered an internet problem beyond my range of resolution. I'm staying at a hotel for a few weeks and their internet is one of those open ones, where you connect with your room number and a given passcode. So I connected all my devices, internet is working just fine (sites, YouTube etc.) until I wanted to feed with Zoe down midlane. I launched my LoL client and logged on, and waited a good 2 minutes whilst it was "authenticating"; until it finally gave up and said "an unexpected error has occurred". I tried a lot of things such as restarting the client, the computer, repairing the client, disabling both McAfee and Windows Firewalls, updating drivers, adding -tcp and -clearbeta to the file etc. I eventually rage quitted and launched some steam games, they launched successfully but when I tried to join the online servers (on Battlerite, Arma 3 and Borderlands 2) it claimed I wasn't connected to internet. From then on I think I understood the problem was with my IP adress, so I downloaded a VPN. That worked, I could play, but seeing as I don't want to pay for one, I only have a few trials before I have no more VPN. So I was hoping one of you lords could help me out. By the way, I'm running Windows 10 on an HP Spectre x360. Thanks in advance, Yours truly, That %%%%ing afk Zoe with internet problems
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