I just thought some of you would like an update on this saga...
I had another look at the set up yesterday - I live a long way away from ma & pa, so I don't get to try too often on this problem. Anyway, it turns out they have an AOl modem that came with the broadband set up

, so I plugged it all in & as distinct from the Belkin router, the internet led lit up. However, the AOL client couldn't see the connection & kept trying to dial in.
So, to cut a long story short, I got rid of all the AOL software (which is a mission in itself), ran cc cleaner & reinstalled it & hey presto, a working broadband connection that is still up 36 hours later.
So, it appears that BT & AOL were in the clear all along & that Belkin were being less than helpful. The next part of the mission is to find a wireless router that AOL likes & works with. I shall keep you informed and thanks everyone for all your suggestions and help.