You *believe* it's connected to the router?! You don't know for sure?
Most DSL users have a combination modem+router. It's actually a modem and router combined into a single device. It will typically have 3-4 LAN ports and an Internet port (RJ11) from which you run a phone line over to the DSL service on the wall.
[wall](rj11)<-- phone line-->(rj11)[dsl modem+router](lan)<-- wire -->(lan)[laptop]
Does that sound right?