Go to control panel > network connections on the computer that does not work fine. Click the 'View status of Connection' on the left hand panel. Then click the support tab and hit the repair button. See if this does anything.
If not try the following:
Go to control panel > network connections on the computer that works fine
In the left-hand window click 'View Status of Connection', click the support tab and copy down all the information about the IP Address, Default Gateway, and subnet mask.
Then go to the computer without the functioning capabilities, and manually set it to use those settings.