I would use Power line ethernet to get the signal to the media cabinet, then use a small 1G switch in the cabinet to connect your A/V gear to the Internet.
Power line Ethernet is cheap - you plug one unit in to a power receptacle near your modem and another near your media gear. Hook your modem to the first unit with CAT5e cable and you will have a working port in the media gear location.
But why is your modem downstairs? I presume you have cable for the AV gear. Why not put the modem in the media closet, use the switch to connect to the AV gear, then have a wireless head near your TV?
Oh, and get your own cable modem. When you lease they often give you older stock because it is cost them less. Amazon or Frys will have great, current models for a reasonable cost, or older models for very cheap.