Ok.
First, by “modem” you mean “router.” I don’t mean to be pedantic, but I’m easily confused; it’s like going to the garage and calling your distributor a ‘rotor arm’.
Second, what do you mean by “struggles with connection” – are you talking about wireless PCs / laptops connecting to the router, or the router holding a stable ADSL connection? Very different problems with very different solutions.
Third, broadly speaking, you don’t need to use the ISP-supplied router unless there’s a specific reason to do so (which I’ll come to in a sec). You should just be able to change the username and password in the WAN Settings config page on your Netgear and double-check that the other settings on that page haven’t changed.
There’s caveats to this. If your router doesn’t support features on your new connection (for example, if the old one is ADSL1 and the new connection is ADSL2+), you’ll not be able to use it (well, you might but at a reduced functionality). If TalkTalk don’t supply you with the ADSL username and password, you can’t use it without hackery and possibly breaching contract (Sky do this, the credentials are hard-coded into the router). If you ever need to ring support, be prepared to swap in their router for troubleshooting purposes.