If you're thinking of operating in the USA, you should read up on Communications Assistance for Law Enforcement (CALEA). CALEA pretty much requires that you be able to associate a name with any IP on your network, so you're going to have a hard time operating as an ISP without any personally-identifying information about your customers.
Regardless, if you can figure out a way to anonymously collect payment for services online without either getting ripped off by your own customers or leaving a paper trail for law enforcement to subpoena, then you have a far more valuable commodity than simple bandwidth to offer. In fact, you would have invented "digital cash", and any number of folks (afore-mentioned law enforcement and tax agencies amongst them) will race each other to control or use it.