What sort of connection do you have? Cable, DSL, Dial-up? Also what commands are you using while scanning?

WinPCAP has some issues with PPP/PPPoE (Dial-up/DSL) connections. Getting it to work can be iffy. I have two systems, both running XP Pro (same upgrades, patches, everything.. could pretty much be ghost images of each other). I have them both on DSL. On my desktop if i attempt to run nmap I'll get no response, or the computer will hang. On my laptop I was getting no response, until i changed my scan type from Syn Scan (-sS) to TCP Connect (-sT). I can run scans using TCP Connect, however I still get nothing with -sS. I can't explain why as I'm still working on that, but in the mean time this may be a work around for you.

Also your router should not be affecting the scan, it's a piece of networking technology, it has the same abilities to send as your computer does. However you could attempt to set-up the computer you are scanning from as a DMZ on your router. That should clear up that issue for you.