Lose Connection To Internet After Several Hours Of Inactive

I have a new Compaq Presario M2105US with XP sp2.My network includes 2 iBooks with airport cards, the Compaq Presario and a Desktop Mac with enthernet connection to my Linksys WRT54G v.3 wireless router. I've got TimeWarner broadband.I can easily connect to the Internet through the Linksys router with all computers. However the Compaq will eventually lose the connection to the Internet (though not to the router) after several hours of inactivity. But only after several hours (perhaps 4 hours or more, but not less than 3 hours). If I use the computer in the evening for example and take several breaks, everytime I come back to the computer and wake it from sleep, it will quickly re-establish the Internet connection. However if the computer is sleeping for hours, like overnight, and I wake it up, it appears to re-establish contact with the router because the network conneciton reports a connection with very good signal strength. But I can't access the Internet. Only by logging off and on again or by restarting can I regain internet connectivity.