No you wont need another router in that case.

To be honest I am not a networking guy but as far as I know your operating system hasent got anything to do with this problem..
Can you check if the DNS settings are the same on both your laptops?

Does your vista laptop pick up the router in available networks or is it not showing atall? Are you using a PCMCIA card for the laptop or does your laptop have an inbuilt wireless lan pci card and if it does does it support 802.11g or whatever is written on your wireless router.
I am sure answers to one of the above questions will sort out the problem.