I believe that, even if you have fiber-optic lines right up to your door, you will still be limited to 56K if you're paying for a dial-up Internet service and you're using a 56K modem. And, you can't magically transform a 56K dial-up service to a much faster broadband service by merely eliminating the 56K modem and getting a DSL or cable modem.
In other words, if you want broadband, which genearlly means DSL or cable, you need to pay for that service and then that's what you'll get. And, I believe fiber-optic cabling by, in the case of DSL, is not necessary for DSL. As far as I know, the local phone company that provides my 3.0 Mbps DSL still has copper lines in my area.