I know it's against adsense TOS. But I have registered a new adsense account after being banned.
I sent in many appeals too and got the same canned response stating they want nothing more to do with me.
To get a new account, I registered a new domain, setup up brand new website, then I waited 4 months before getting the new account so I'd have time to get the content up on the site and drive traffic to it.
Plus it gives time for things to cool down on your old adsense account.
I entered my same address, same payee name, and used the new domain.
A few days later I was approved in the first step and then after adding the code to the new site I had a fully activated account.
So far in a year I've been getting monthly payments from the new adsense account.
So yes. Although it's against the tos to open a new account, you can get a new adsense account and still earn money through them.