Can you run a ethernet cable to another modem then connect that with more comput

Polylogy

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Aug 12, 2011
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Hello,
We lost our IT guy over the summer and I am trying to set up a subgroup of computers in my classroom for classroom research. I could make and run the appropriate number of Ethernet cables to each computer but they would have to be fairly long and go over/under a doorway across my back wall/over counter/work area. I have found a small modem that I was hoping to just run one long Ethernet cable to then have it on the counter so that the computers could be connected to that modem, is that possible? We server on other side of building, a Dell Powerconnect switch box in my storage closet that I will connect all the computers to and the small modem is an Intellinet network solutions box. my computers recognize the internet when connected through modem but even though it reads 100 kb/m it also says "limited/no connectivity" we do have wireless internet but it only reaches the other side of the building. All computers are Different DELL laptops with XP on them. Ideas? Suggestions? can it be done?