several things that could be happening:
1) ethernet cable is damaged , try swapping it with the other ones to find out if this is the case
2) lan is not enabled on the third computer. go to start>control panel>network connections.
see if lan is enabled. if not
right click on lan, go to properties, click configure, then in the drop down box choose 'enable'. this should enable it.
also if the third computer has a wireless, it could be interfering. follow the same steps above to disable the wireless.
for games you might run into these problems:
1) different versions of the game. update them all.
2) firewalls. open up the firewalls for the game.
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