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A switch will not work in this instance. You need to be using a router.
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The cable modem will only speak to one device at a time. It can only see one computer. The second one will be invisible. If you power off the modem and first PC, power up the modem and laptop only, then the laptop should work but not the PC.
A router knows how to communicate with the modem and the modem thinks a router is the computer - it doesn't see past the router. The router on the computer side, sets up the network protocols so that both computer and laptop can work alongside each other. A switch is just a junction box.