Resolve DNS

I just set up a wireless network in my house with both my 2 computers. I'm
mainly just sharing the DSL internet connection between them. However, I've
had connectivity problems since I've bought it. I contacted the maker of the
router and they checked everything with the router and wireless adapter and
said everything was fine but that I needed to contact Microsoft and tell them
I need to Resolve my DNS. I'm not sure what that is but it's preventing me
from browsing on the internet on the computer that's hooked up wirelessly.
The connection is fine for 5 or 10 minutes when I connect, but then I can
barely visit webpages after that. I have to refresh them multiple times just
to load them once. And even then, they're lacking things they should've
loaded. Before I had this wireless connection, I had dial-up and it would
only let me browse websites for a few minutes and then I wouldn't be able to
visit any sites until I disconnected and connected again. Yet in both cases,
wireless and dial-up, I was unable to browse the internet even though the
connections remained connected. I don't think I had this problem until I had
to format my computer and reinstall XP Home a few months ago. Please help me
if you can. I'm really frustrated with this issue.