Reddit will be your friend here. Find a way to somehow proove that you didn't bot, then make a public announcement and shame jagex for it. If you're lucky enough you'll get noticed. Was a while back when I read about some kid trying runescape out for the first time, he got banned within a day a day and jagex blamed it on inexperienced moderators.
Since this was a manual ban they might review it.
It could also have been a delayed ban back from the golden ages, they tend to do this with people who've been caught and then as soon as they pull out their credit card get banned. Happened to my IRL friend a while back.
Feel free to ask me any questions, I will do my best to answer them!
Previously known as YouPee.