Can a laptop with a modem card be connect to a router to provide
internet to other computers?

I know of at least 1 way to do it that is quite easy to setup under windows:

1. Go to Control Panel/Network Connections
2. Right Click and select PROPERTIES on the Network connection
associated with your modem.
3. Selected the ADVANCED tab on the top (there should be
General/Authentication/Advanced as options)
4. Select the box that says 'Allow other network users to connect
through this computers internet connection'
5. In the drop down box, select the Network connection you will share
on...this is likely your ethernet/lan connection that you will plug
into the router.
6. Plug the network connection/ethernet connection from 5. into the
WAN port on your router (this is the same place you'd normally plug
the internet connection from your cable modem/adsl modem or other
internet source)
7. As long as your router is configured correctly, to use dhcp to
retrieve an IP address, you can now plug client computers into the
router.  The router will grab an ip address from your host computer,
and will assign new ip's to all the client computers connecting to the
router.