Hi, Richard Farish
It sounds like the box from GCI may be a modem only, without Wi-Fi. That would explain why the internet works over the cable but no wireless network shows up.
Look at the sticker on the back for the model number. Some GCI models, like the Sagemcom FAST 3893E, Hitron CODA-45 and Hitron CDA-3, are listed by GCI as plain cable modems. With those, it is recommended to pair the modem with a GCI Wi-Fi pod (a small Plume SuperPod), which creates the actual wireless signal. GCI provides the pods to internet customers at no extra cost.
If you have a pod, or GCI sends you one, the setup is simple. Run an Ethernet cable from the modem to the port on the pod marked with the special icon, then plug the pod into a power outlet. After that, log in to the AK-Fi Home app with your MyGCI account and finish the setup there.
If you're not sure what you have or you didn't get a pod, call GCI at 800-800-4800 or chat with them on gci.com. Ask them for "a Wi-Fi pod for my cable modem."
Once the pod is running, your other computers should see the new network and connect normally.