The lights on the back of what...? Your router? If there is a problem with your router, technically it should affect all computers attached to it.
For example, I have one wired PC, one wireless laptop and one iPod Touch connected to my broadband router. Sometimes I lose my broadband signal [the light flickers] and my computers would lose their internet connection straight away, but my iPod stays connected to the internet, for some odd reason.
I'm not sure if your problem is exclusive to your PC or whether it's your router that's acting up, though.