Internet connect problem

Hello! This is my first post to this site. I have a DSL connection and when I try to connect to my ISP from an iMac G3(panther 350MHz) and an iMac G5(tiger 1.9GHz) simultaneously through a 3COM 8port switch, only one of them connects while the latter - whichever machine might be - is rejected.I mean that when any second computer tries to connect, it is rejected.I think that it's a matter of network configuration. The two computers can exchange files even with laptops using appletalk.
I have tried to configure DHCP in vain. Same with internet sharing.

Thank you in advance

If both of them will connect no issue - and only problem is that you can only connect one at a time - would look to the router - check for setting that limits # of IP addresses it will hand out at a time

Have mine limited to the # of computers in my house, just another prevention tool to keep outsiders from trying to access my wireless network.