|"You may need more than two wires connected to get the phone to ring."|
You only need two.
The residential cords have 4 wires but it's only essential to connect two. Take a look at the clear plug - for most phone cords, except at some businesses where they have call holding available on phones, or two lines on one phone (and 4 or 6 wires/contacts) , there are only two contacts, two wires connected to them ( or 4 contacts, two wires connected to the center two contacts).
If there are more than two connected on the original cord inside the phone, let me know, and I'll look inside my phone to see what must be connected. In North America, the the colors are often labelled beside the connection - B(lack), G(reen), Y(ellow), R(ed). If the wires in the plug are wired up and colored a standard way, you simply connect the proper color to the properly labelled connection (appears to be red and green, standard, from several cords I looked at) .