Cannot access network computer without internet connection

I have 3 computers running Windows 7 Ultimate x64.

I connect them to a hub and set a workgroup name. Everything is working fine. All of them are able to see each other and access their shared drives.

However, once I unplug internet line (all computers still connect to the same hub), computer cannot see each other and cannot access shared drives anymore. Also, workgroup name is changed to 'Unidentified Network'.

What should I do to connect to a network without internet connection?

Thanks

Network hubs are literally archaic. I hope/presume you're using a switch.

There's ways to make this work but you need to do something about your network topology first as what you've described is hideously insecure.

Do you have a router between your switch and your Internet connection or is your ISP giving you three IPs when you connect your 'Internet line' to your switch?

I'm really sorry for any unclear information. I don't know much about this stuff and English isn't my first language.

Yes, by hub, I mean a switch. Also, I have a router and it is connected to the switch, and the switch is connected to 3 computers.

Someone told me to assign a static IP to each computer. I still have no chance to try it yet. Do you think this would help?

Thanks a lot

Everything should keep working if you disconnect your Internet connection upstream of your router. For instance, remove the cable between the router and your modem rather than between your router and your switch. If your router has an integrated modem, disconnect the incoming phone or cable TV line from the router.

Windows will see an 'unidentified network' and disable file sharing on any network adapter that doesn't have a default gateway set. As long as the computers can see your router, they should be satisfied that they're on an identifiable network. If you disconnect your router from your switch, however, they will conclude they are on an unidentifiable network.

Why do you want (or need) to disconnect your Internet connection?