Wrongly banned, has this happened to anyone else? Did you get your account back?

A couple days ago my account got banned, for apparently the use of 3rd party programs or exploits. I've never used anything to try to make any changes to the client, or to cheat in any way. My account was compromised a few weeks back, and so I just assumed that whoever had hacked me had done something against the rules. I e-mailed Riot about overturning the ban, but I was told there is strong evidence to support these claims against my account and that there was no unauthorized access that is related to the exploiting. I was also told they can't reveal any details to me, so there is no way for me to defend myself basically. I don't expect everyone to believe me, but for the sake of discussion I'd like you to at least think from the perspective of someone who is telling the truth. The only programs on my computer are video games, Skype, and Word. There's nothing on here that I could cheat with. I don't even know how to fucking cheat in this game. I don't know about exploits, or hacking, or anything like that, I wouldn't have the slightest clue how to do it if I wanted to. But here I am, being told there is strong evidence of me doing so. What should I do? I've e-mailed them back begging them to look into it further so that they will hopefully see I've done nothing wrong here. Idk what to do from here, I don't want to give up because I've had my account for like 5-6 years and have put so much time into it.