diagnosing DNS problems at router level

I'm using Windows XP sp3 in a house where I rent a room. We have wireless service to a router the landlord controls. Recently I'm having sporadic problems resolving URLs. For example, one day I can get to google.com, and the next it won't work unless I have an IP address. No one else in the house has this problem. When I put my PC in the shop, they had no problems the minute they connected to their ISP. Got the PC home and it was working again. Then it went out, then it came back. Are there DNS diagnostic tools I can use? I tried NSLOOKUP from the command line but it wouldn't let me use DIG. Very frustrating. The little network monitor always shows a red X between the router and the Net when I'm having problems. Today it's a green dash and everything is OK. For a while.