How do you explain the problem I had with an Internet connection?

I bought a new computer, but it did not recognize my Internet connection. The Ethernet light on my modem did not go on. Using the same setup, I have no problem connecting my laptop computer. I brought the computer back to Best Buys, where I bought it. They were able to connect it to the Internet using my cable. Their suggestion was to check with Verizon, who provide my DSL connection. Instead, I returned the computer and bought one from a different company, which I am now using to ask this question.