How can I manage the wired connection on the AirPort Extreme?

I use both wireless and wired connection on my AirPort Extreme. The wireless connections work great. But when my Dell computer that is wired to the AirPort Extreme hibernates, it loses its connection to the internet. It remains connected to the AirPort Extreme, but loses the connection to the internet on the wired connection (back to the cable modelm). At this point the only solution seems to be to restart the Dell computer, which takes forever. Any wireless connection remains fine. Trouble is this Dell computer is reasonably fast on wired connection and fairly slow on wireless connection, or I'd just switch it to wireless connection too. Any ideas?

AirPort Extreme

AirPort Extreme

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