Thanks for those.
I'd found the B/G/N/Mixed one and tried that. It made no difference.
Both machines are running Windows 7 - the laptop is Ultimate 32-bit and the desktop is Home Premium 64-bit. The old laptop, which ran Home Premium 32-bit didn't have the problem.
Connecting the Cat 5 cable from lappie to router means the network map works. If I then switch off the lappie and leave the cable in, the network map stops working.
I've installed NirSoft Wireless Network Watcher, and it does the job well - thanks. The advantage of the Windows one was that it gave a quick check on what was or was not on line - usually the printer, but in earlier days the laptop when it was out in the workshop and supposed to be monitoring something.
I didn't realise Windows 8 had dropped the facility. That may be an indication of an underlying problem.
I'll leave it at that. Thanks again.