Listen to Tommy. Update the graphics first.
You had 2 applications which stream the video (LoL and Youtube). That could be the internet connection.
Try http://www.speedtest.net/to see if the speed meets your expectation and what you are paying for.
Skyrim runs locally so it doesn't access internet, which leads me to believe it isn't an internet problem. Since the other two don't access disk much, that leads me to beleive it isn't a disk problem
Do you guys have a virus checker and popup blocker on the system. Some malware will slow down your computer in order to trick you into buying services to speed it up. You might want to run a Virus check to see if there is anything there. My ISP provides a Virus checker with the Services, maybe yours does also if you haven't got one installed.
Did you guys restart the machine? Sometimes windows updates need to be installed and that slows the machine and is a real pain in the ass