To be clear, Ethernet cable has no bearing on whether a connection was/is dial-up. It just means that it's a wired connection instead of wireless (WiFi).
At that time WiFi wasn't super widespread, so it wouldn't be super surprising if a laptop didn't support it. Especially if the laptop itself was a few years old.
With enough speed for youtube, you probably had some form of DSL, coming into your house through a coaxial cable, into a coax modem, then back out through ethernet cables.