Banned Account without motives?

Hey all :)

So I was just wondering if there's anything you guys recommend I do/say to try get my old banned account back. So last year i let a friend play on that account and it received a 2 week ban for sharing accounts, i have no problem with this. I was in the wrong, i take full responsibility. Then out of nowhere about 4- 5 months later I wake up nice and early to start my ranked games only to find that account has been permanently banned. When i asked they simply stated i was scripting.

Now I have never used any scripts or any external programs but unfortunately Riot doesn't believe me. When i ask them to show me what i was doing they reply telling me they can't give that information since i can tell people not to use those scripts because they will be caught. Anyway, this is what brings me to my question, Riot employees wont listen/talk to me about this subject, they wont prove nor help me understand what was causing them to come to this conclusion.They refuse to help me whatsoever. What can i do to get that account back?

Thanks :)