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You can only have one device (computer or router ) directly attached to the modem at any one time - all other wires must be disconnected.
You must power off and on the modem if you change the computer or router connected.
---------- Post added at 19:28 ---------- Previous post was at 19:27 ----------
If you do want to be able to use two different computers easily swithcing between both then a router is the simplest option. See the networking thread areas for advice on that.