Can't get Internet Connection Working Properly on Vista

My machine runs Windows Vista Home Premium, is brand new, has 4 or 5 months
and I bought a new modem ADSL2+. It's an Ethernet modem, by the way, D-Link
DSL-320T. I called my ISP and got the configuration details that I put in
modem's menu. However, in Vista, the two computers in the bottom appear most
of the time without the little plante on little and even when it appears, I
don't have connection. But, If I connect this modem to my other computer,
that runs Windows XP, It works really fine. The bizarre is, when I
disconnect it from that computer and quickly connect it to Vista, I have
Internet in Vista!! Thoughts???