How to PLAY LAN NO INTERNET BUT WITH A ROUTER AND ETHERNET CABLES?

It ought to work if it worked at home, providing you are using the PC/LAN Ethernet ports on the router and normal straight cables. Just because there's no Internet service should make no difference except that there will be no Internet access.

Try turning off the firewalls in the computers. If you are not on the Internet and you trust other computers on your private network then this should be quite safe. Just remember to turn it back on when you go home.

An alternative might be to use the phone's hotspot for both computers, but with the mobile Internet turned off in the phone. You might get an odd message on the phone saying the Internet connection is off, but it is worth a try. I have transferred photos between my phone and my laptop using the hotspot but with mobile Internet disabled. I haven't tried it between two wireless connected computers using the hotspot, but it might work.

Finally, if there are just two computers involved, you could use a cross-over Ethernet cable directly between the computers. A local store may have such a cable that is not too expensive. You will need to configure static addresses for the Ethernet adapters in the two computers. I suggest the following:

Computer 1: 192.168.1.21
Computer 2: 192.168.1.22
Network mask: 255.255.255.0

Gateway and DNS server addresses can be left blank.

Rather than using an Ethernet cable, you could try setting up an Ad-hoc wireless network between the computers with static addresses as above. It's a bit messy in Windows 8, but earlier versions should not be too difficult.