Hmm. That's weird - has to be something to do with the wireless, I guess, but does it hapen with the 'new' lappie unplugged rather than 'switched off'? Are you saying it does or does not occur with the 'new' lappie switched off but wired? What OS is the lappie running cf the desktop?
The closest I can get with a wifi only problem is this
"Looks like I found the cause of my problem. The Cisco WRVS4400N Router supports different wireless modes - "G-Only", "N-Only", "B/G-Mixed", "G/N Mixed", "B/G/N-Mixed". When I was having the problem, the mode was set to "B/G/N-Mixed" (which is what I would really like to have). When I changed to "G-Only" or "B/G-Mixed", problem disappeared!! Something different in the "B/G/N-Mixed" mode. Note that while I was having this problem, I did not experience any network connectivity issues between PCs - they could all talk to each other - it was an issue for the Network Map creation only .
BTW, I have the latest FW version for the router."