Route existing network connections to new location?

Question

This is a home situation. Have 20 devices throughout the house wired into the basement into a HP gigabit switch (with support for 2 fiber connections). Switch also has my router/cable model plugged into it for internet access. This is a J9450A switch. I am setting up a server rack for existing equipment in the basement and moving all of it from one side of the room to the other. Problem is the current cables that run from all over the house into the basement won't quite make it to the new location. Was originally planning on taking the switch and putting it in the server rack and running all the cables to the other side of the room into the rack. Many cables won't make it. Can't run all new wires as a lot were run while remodeling and all the walls were down.

Is it better to leave all the cables wired up in a switch at their current location and run fiber to another switch in the server rack to extend the current network to the devices in the rack? Or is it better to do something else to get network support to the rack equipment? I could move the router/cable modem to the new location or leave it where it is now depending on what makes more sense.

Thanks for the input.

JR