I don't think it would be a router problem. The laptop is the only thing that's affected. Xbox, iPod, and all other devices still work fine.
I don't want to come across as an ass, but I can't stand when people give this answer. You're asking for help, but dismiss possibilities. Clearly there's a problem somewhere, and I'm asking the question for a reason. I'm asking for the router make (and model if possible) because you may have a wireless card in your PC or on your motherboard that is using a signal type that isnt the same as the signal your router is outputting.
So, for instance--and to put it into it's simplest terms...Your router is putting out wireless B, but your wireless adapter in your computer is a wireless N adapter. The adapter would then operate as if it was a wireless B adapter, and will be noticeably slower.
I followed that tutorial about the DNS but it didn't help.
I didnt think it would help, but it was worth a shot.
Also, if you could run a tracert to youtube and see if there are any failed hops along the route (specifically at the VERY beginning of the route, where your computer goes through the router), then let me know.
To run a tracert, open a command line and type tracert www.youtube.com
Any instance of * in a line indicates a time out.