I've seen this before on a Win98 box and Win2K box - my solution was to ensure that I was logged in as the same username on both boxes, as phishphreek80 stated as one of his ideas. My guess is that the router isn't going to have anything to do with it, it's more of those mysterious things that Windows does.

You might try disabling the Norton firewall for troubleshooting this issue, but it shouldn't hurt to have it running normally, even though your Linksys is acting as a firewall. The more security the better in this case...