What may be the problem???
Hello and welcome to the forum.
I suspect this problem is due to your ISP and how it handles DHCP leases for your network connection.
Sometimes it can be resolved by releasing your DHCP lease on one device before connecting the second, other times it's a matter of waiting for the lease to expire before you can obtain a new lease for a new DHCP connection to your ISP before you will be able to get the second machine connected.
That is why it's a good idea to connect a router directly to your ISP's device (assuming it's not a dialup) and configuring the PPPoE details on the WAN side of your router (user name and password) and then you can connected multiple devices (computers) to the switch ports of the...