There are many......many ways that an Ethernet network could be configured as far as Internet connectivity. However, there are a couple of layouts that are extremely common -- probably used by something like 91% of home and SMBs. I'm going to assume your using one of these more common setups but unless there's more detail that you provide (home? business? high speed cable? DSL? windows who? Linksys router? D-Link router? Netgear router? No router? Hamster running inside wheel? etc.).... um, this answer will be a tad generic. But luckily generic stuff usually works.
Although my expertise and experience is with the Vaio, these troubleshooting steps apply to any PC running late Windows XP. I'm also assuming that your method of connecting to the Internet goes something like this: Ethernet cable from your laptop connects to a switch/router (doesn't matter if its standalone or integrated into a router, as long as the connection gets to the router that is plugged into your broadband service) --- router connected to a cable/DSL modem (some DSL providers sell a combo router/modem unit... might be made by 2Wire, for example) --- modem interfaces your internal gig with the Internet... happiness occurs as long as nothing breaks.
1. Start > Connect To > Show all connections
2. Unless you renamed it, your ethernet network card that's built-in to the Vaio will be represented by the icon entitled "Local Area Connection" -- and it sounds like you already know this. I apologize in advance if I go over or under your head.
3. Left-click "Local Area Connection" and then in the left sidebar of that window (where you see Network Tasks, Other Places, yada yada...), collapse all of the categories except for Details, that way it's right there and you don't have to scroll to get to it. What does it say?
A) If it says "Disabled" then go over and right-click Local Area Connection > Enable. Or if you don't even see the "Local Area Connection" icon then your card isn't being recognized and you can just read on because I explain how to download the driver (even though that is a generic first-step solution).
B) If it says "Network Cable Unplugged" then try another cable, check connections everywhere (does the light on your router/switch light up for the ethernet port you plugged into?). If all looks good then the last generic thing you can do besides replacing hardware is go visit this little linkeroo:
...and plug in your model of Vaio. Look on lower left corner of display panel, DON'T use the "model number" listed on the bottom panel... or else the computer may display a very large and disturbingly lifelike image of a middle-finger!.... ok kidding there... it won't be the middle finger per say.
...............Now download the drivers for the network card/controller by clicking the + symbol next to the category and then hit the green arrow -- and choosing RUN when prompted is totally and completely acceptable, and even highly recommended.
C) If it says "Connected" and shows an IP address that begins with something other than 169.xxx.xxx.xxx
, then you may be reaching the router and I'd check your Internet connection. Call your ISP? Check router config... Maybe feed the hamster if he's hungry so he can keep spinning that wheel? These are all valid suggestions.
4. Try this: Right-click "Local Area Connection" and select REPAIR. This will release the IP address, disable the network card, flush DNS, restart the network card, re-register DNS, and ask the DHCP server (probably the router) for a new IP address, which is basically the computer's phone number.
5. Any third part software installed for security purposes? Like Norton Security or some other firewall software? If yes, get rid of it... see what happens.
6. And step 6 would be to start drinking... or provide more detail. Obviously you got on the Internet somehow or else you wouldn't have posted the question so go use that connection and check out the very user-friendly and sophisticated Sony support site -- again, the link to Vaio support is http://esupport.sony.com/perl/select-system.pl?PRODTYPE=1,24,26,66,9,70,5,72