I need to unplug all connectors of my modem and keep it few seconds and reconnect all to access internet?

What I'm wondering with this modem, ( which I'm unfamiliar with ), if the battery backup holds the settings even though you've unplugged the power cord. Maybe you could remove the batteries and then try the same procedure to see if that allows for the second computer to be recognized. Then you can reinstall the battery backup. I know on my modem, I was told to disconnect the power cord after the internet connection and the Ethernet cable and reconnect the power after the cable connection and the Ethernet cable. They told me the improper sequence would cause problems. Power cord always last to be dis-connected and re-connected. Hope this information will help to solve your problem. That's all I can think of to try. Good luck!