You are trying to use a "Network Switch" as a router and it isn't going to work. Your ISP only allocates one IP address and this will go to the first PC to connect. The second PC has no way of getting an IP address and Windows will allocate a default APIPA address (Automatic Private IP Addressing) in the 169.254.x.x range and this will give the "Limited or No Connectivity" error indication.
Because the first PC is getting a WAN (Wide Area Network) address from the ISP, you cannot even network the two PCs via the 'switch' because they need to have LAN IP addresses.
1) Replace the 'switch' with a router. This connects directly to the ISP and gets the single IP address. In turn, it allocates LAN IP addresses to the networked computers so they have internet access over the LAN from the router and are also networked for file and/or printer sharing.
2) Install a second network adapter in the first PC so that one is used to connect to the internet and the second connects to the other PC. Enable "Internet Connection Sharing" on the network adapter that connects to the modem in the first PC and the second PC will have internet access, provided the first PC is online.
3) Connect the first PC to the modem by USB and connect the two PCs via the network adapters. As per (2) above, "Internet Connection Sharing" would have to be enabled on the connection to the modem.