if your computer is using your internet bandwith then it will have some sort of impact of the speed that web pages load. the amount of impact it has depends on how bandwith the is being consumed.
As a general rule your computer should only be using the internet in the background to update Windows, Anti-virus software, spyware software etc. if none of these are being updated and your connection appears to be in use then you "may" have a problem.
First thing that i would check if i suspected something dodgy is to check the network adapter usage, this can be done by using windows task manager (or a network monitor), task manager will show you the network adapters that are present and it will show you the amount of bandwith being consumed in the form of a percentage.
if the computer is idle and you are not using any apps that access the internet and nothing is updating and bandwith is being consumed then if you haven;t already it may be worth installing a software firewall on the computer, what this will do is notify you everytime an application or nasty ass trojan horse tries to connect to the internet, this should help you establish what is consuming the bandwith.
