NTL do block ports 1433 and 1434, is there any way that you can specify alternative ports within your software.
Also, you say you can *add* a cable modem to the setup. Unless this CM was obtained from (and registered with) NTL it a) wouldn't work on the network and b) it would be against the terms and conditions you signed up to c) may be illegal depending on where you got it from.
On top of all of that, you would find that adding a Cable Modem to your setup wouldn't solve your problem. That port is blocked by NTL regardless of what type of modem you use, unless you are on a business account of course

__________________
Hmmm.....
I just read the above post again.....
Are you having to specify an IP/MAC address anywhere in the setup (either server end or client end) that facilitates your connection to the SQLServer?
If so have you checked that it still matches your current IP/MAC address as these will certainly have changed when your box was changed.