Actually, all functionality on the Internet is dependent on IP.
I won't get into specifics of the OSI model and how things work in great details, but what I can assure you is everything on the Internet communicates via IP addressing.
Dial up simply establishes a connection (called a Link Layer or Layer 2 connection between two points, your ISP and your home PC via hardware communications between your modem and the dial up gateway at your ISP) However, it has no idea what to do next. It becomes dependent on the Network Layer or Layer 3 for addressing and path determination. Essentially, what is my address and how do I get to the next address so how does your PC find iboats.com.
While not as evident as with other technologies that people are more comfortable with such as high speed cable or DSL, it all works on the same basic principles.