After playing since pre-season 1, my 6+ year old account was falsely banned... What can I do?

I started up league ready to play the same way I have been playing for over 6 years and was greeted by a lovely message, "Hello Summoner, Your account: theaussie1991 was banned due to the use of malicious 3rd party programs or modifications to your League of Legends client." I thought surely I had messed something up, it was a bug, or a joke... and then I quickly realized how serious it was. The account I had been using since before season 1, on the same computer, with the same installation folder, had been permanently suspended. I felt sick, thinking about the thousands of hours played, hundreds of dollars spent, all my friends and contacts destroyed. I guess I never realized how important this account was to me, and how insane/scary a false ban can be. I seriously need help, I've messaged Riot through support and received no information or assistance pertaining to my ban. I have never hacked, scripted, exploited, or downloaded a program to give me an advantage over others in ANY game in my life. I could write for hours about how insane this situation is but I just need guidance, where do I go from here? I appreciate any help! I could copy-paste my talks with support about it but I don't know if that's allowed. They have said "I know you have some unanswered questions about your punishment which I know is frustrating. However, I won't be able to give any specifics as this will compromise our investigation process. "

What do you do when you have never hacked, have no idea why you're banned, and aren't told why you are banned. I'm not giving up on this account, it's incredibly dear to me. Every response has basically been "bad luck, we're 100% sure you're hacking but can't tell you anything about it". It's ridiculous. I can't just be content with that response.