My guess is that your modem is a combination modem/router, or what the ISP probably refers to as a "gateway"...

Its probably handing out an address to your equipment in the same subnet as your ATA's lan side...

Your Belkin most likely uses another subnet and therefore has worked ok.

You can try changing the address of your ATA or put your modem in bridge mode. (my personal choice).

So that why the request for model numbers...