|Your Internet Service Provider likely gives you 1 IP address. It's passed to your modem which then sounds like you have plugged into a switch. If that's the case, it sounds like the computers are fighting over that 1 IP address, so only one can connect at a time. What you need to do is instead plug a router into the modem and remove the switch. With the DHCP server option enabled on the router, it will be able to assign network IP addresses to the 3 computers, and all will be able to simultaneously use the 1 external IP address given to you by your ISP.|
A router performs like a switch but has many more features. Even wireless routers have ports on the back so you can have some computers on your network connect wired while others are wireless. The switch doesn't seem at all necessary in this setup.
"When each are connected one will not have internet access. Turn the computer with access off and the other gets access." The computer turned off "leaves the fight" so the computer still on can easily grab your 1 external IP address. If I'm mistaken in your network design, please thoroughly describe it.
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