Yes you will need wireless cards for the PCs, but you can get away without a wireless router.
On the machine with the modem attached, just use the wizard to set that up as an 'access point'. All the other machines should then network with that machine.
The problem is, if you do this, that one PC will need to be on all the time. A wireless router would avoid that, as you attach the modem to the router instead.
Post again if you'd like a quick sketch or two