What to do if you're permanently banned on a Minecraft server?

Nearly a year ago, I was banned from my favorite server, which I had been on for over a year. Despite not having any hacks, the staff still claimed that I did. I'm banned from the service website, because my ban appeal was denied. Basically, there's no way I can go back there on my old account. I've tried using other accounts, but since I'm IP banned, those got banned as well.

How can I still play on this server? Would I need to get a completely new router? A new computer? I know I'd need to make a new account, but I'm not sure how I could bypass the IP ban.

Added (1). I don't want to join another server. This server was completely unique, and every single server that's even similar pales in comparison.

There are thousands of awesome minecraft servers. If they perm ban you for hacking when you're not, it doesn't sound like a good server in the first place. Definitely not a good enough server to spend a lot of money on to get back on.

Join another one

Connect to a proxy server on your computer and a different mc account and you should be able to get on then