Dropped Internet Connections

I have Aol 8.0 for my ISP with a dial up connection. Everytime I try to connect to the internet it will go through the process and then says unable to connect. My computer is a two yr. old Hp with an internal Lucent modem. What could possibly be the problem? I’ve done a systems diagnostics and itsays the modem is fine. Other than the phone line what else could it be to drop prematurely?