How do you connect both networked computers to the internet?

The switch itself. It sounds like the switch may be having a conflict between any two given NICs. And as for plugging the modem directly into computer #2, did you use a cross-over cable or just a straight cat5?

Because if you are connecting anything (two computers, one computer to a modem etc. )without going through a switch or a router, you must use cross-o.

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