BleepingComputer.com: Internet connection problems on new computer

We have a new Sony Vaio laptop running Windows Vista Business 64 bit, with an Intel WiFi 5100 AGN wireless adapter, and it is connected to my home network through a Linksys WRT54G router on a cable modem, but we have trouble with the internet connection. Either it will randomly disconnect from the internet (and shows local access only), or sometimes it won't connect to the internet at all. Sometimes it will reconnect after restarting the computer, and sometimes it won't. It may stay connected for a couple of hours with no problem, or it may not. We use Firefox 3.5.2 for web browsing, going through Google to videos, and other web sites. I am wondering whether the problem is the business OS or the 64 bit as the other computers on the network are using XP Home Premium, and Vista Home Premium, both 32 bit. Neither one has any problem staying connected. The anti-virus in the Sony is Webroot with SpySweeper, and the Windows firewall is used on all the computers, although they each have a different anti-virus program. I have been trying everything I can think of to fix this, and several times it seemed to be working fine, but then it would go off again. Also there are a lot of security features in the business application that are not in the others, and I don't understand some of the terminology in them. Can someone point me in the right direction or at least tell me what to check before I give up and take it to a repair shop?...Please... I am tired of trying to figure it out on my own.
Patti