Playing games randomly disconnects the internet

I've searched with Google for someone with a similar problem, but I can't appear to find anyone with the same problem.

Okay, here's what happens: The internet runs fine in Internet Explorer or Firefox. And I can use it for as long as I want to. However, whenever I turn on a game and play online, the internet will randomly disconnect and not allow me to reconnect. Unplugging my wireless adapter does nothing, and the repair feature etc. does not work. In order to get on the internet, I must reboot.

I'm running Windows XP SP2, and I've tried uninstalling SP2 to see if that works. It doesn't, and so I've reinstalled it. I've tried turning off any firewalls that might be running, but alas, it does not work. It's really starting to piss me off, as Xbox Live (which is hooked up by wires) works perfectly well for any amount of time. The other wireless machine is a laptop, but it's old and I've never played games on it.

Wireless is the only option for me, as this computer doesn't have an ethernet port. I could get a card, but I'm going to get a computer in the near future so why waste money on parts for an old computer? I've got a Linksys network adapter, model # is WUSB11 ver 2.5. Router is also a Linksys router.