DNS problem with broadband router + Vista

Problem: unable to access the internet through a broadband router with Vista.

Setup:
Vista PC connected to 4-port broadband router (speedtouch 536).

Details:
After installing Vista, I found that my PC was not able to connect to the
internet, because it was not picking up IP addresses of DNS servers from the
broadband router. Normally (eg Windows XP, Mac OSX) when I plug a computer
into this router, it is assigned an IP address and picks up DNS servers, all
automatically.

With Vista I had to manually configure the PC's LAN network connection DNS
servers using the IPs specified by my ISP. I would have thought that the
process of picking up DNS server addresses would all be part of a standard
protocol (DHCP?) and wouldnt for example require any special Vista-specific
drivers for the router. So Im assuming there is some configuration problem
with Vista (out of the box!) which prevents it from working properly with a
broadband router.

Also, normally, when connected to the router, the router's admin web server
can be accessed at http://speedtouch.lan, so presumably the router's own DNS
isnt being accessed by the PC?

Does anyone have any ideas how to fix this problem?