Thank you one and all!!
Apologies for nor responding earlier but (you've guessed it!!) the &$*!** internet link went down AGAIN. Having gone from AOL to BT to Tiscali and now to Orange I despair of EVER finding an ISP which can provide RELIABLE service.
Anyway, I have now drilled large holes through two walls and moved the router one room nearer to the second machine, the signal shows a constant excellent. I spent so long on the phone with D-Link trying to sort out the network that the phone battery ran out and I was cut off - WITHOUT getting the network set up!!!
Have just rebooted this second machine and - Glory Be!!- I have got on line from it.... absolutely no idea what has happened/changed.
I shall try to work through the various helpful suggestions and see if I can make any sense of it.
If this internet connection ever happens again, I will report back.
Thanks again