BSOD When 2 Computers Connected To Wireless Network

I've got a Sony Vaio labtop I bought 10 months ago in the US. I'm in Australia now but have no international warranty. Sony tells me to send the labtop to Sony repair so they can look at it. They trouble shooted over the phone but it didn't help. Asked me to reformat the hard drive which I really don't want to do. This is the problem:

The computer works fine and I can connect and browse the internet with my wireless connection. However, as soon as I connect another computer to the wireless network (or if I'm in a hotel using wireless it also happens because other computer are connected to the same network) I get the BSOD.

The problem is that I cannot say exactly when it happens. SOmetimes it happens within 1 minute of being connected and browsing. Yet sometimes it takes 20min or maybe 45min. I don't think I survived longer than 1h though with 2 computers on the same wireless network.

I didn't notice the problem at first because I only used the one computer. So, I think the problem has always been there but I didn't notice it until I connected a 2nd computer.

To get the blue screen I don't even have to actively browse. I could just scroll down on a page and it happens without warning.