The Linksys phone "system" comes with a handset (and charging cradle), and the "base station" (the thing that is essentially the "system", rather than just the handset).
The charging cradle has on one cord, and it's attached to the cradle. That's the cord that plugs into an electrical outlet in the wall, or on a power strip, and provides the current to charge the handset.
The base station has a place to connect the USB cable to your PC, and that place on the base is marked, "power". Your PC provides the power to the base station. Also on the base station is a place to connect a phone jack for the second line you want to use with the system. That USB cable will take care of all Skype calls. The second phone line is what you'd use if you want to connect your landline, or the MagicJack line, to use as "dual part" of the two-line phone system.
To use MagicJack with the Dual Telephony phone, you'd have one end of the MagicJack cable plugged into MagicJack; with the other end of that cable plugged into the base station (instead of into, say, a "plain, old, phone").
Before giving up on the corded phone, you may want to double-check the audio devices to make sure your mic (recording) and speakers (playback) are set to work with MagicJack. Go to "Control Panel" and then "Sound and Hardware". From there go to Audio Devices". The only way to check which speaker/mic is set to work with which USB port (or other device) is sometimes easiest just by trial and error. (In my machine, the Linksys name shows up immediately, but not other hardware).
(The cord that runs from the "power" connection on the base is the cord for Skype calls. The other cord (the one with the conventional phone jack) is the one for either landline or MagicJack calls.)
Something else you may want to double-check is whether your firewall(s) may be blocking access to MagicJack. From "Control Panel" go to "Security" and then "Allow a Program Through Windows Firewall". From there it's generally self-explanatory, although if there are other firewall-related issues you may be better off going to MagicJack's online technical service help.
If you haven't done this already you may also want to just uninstall the first MagicJack installation, and install it again.