It should be able to locate you wrt to the towers as well. My GPS works fine but I can turn GPS off, run "Maps" "My Location" and then it gives a pretty good estimate of where the tower is that I'm using. I compared that against online tower databases and it makes sense.
If you are outside and not substantially blocked from the sky by buildings, tall hills or very thick trees, you should get GPS location. If not, I agree that it could be a hardware problem. It sometimes takes a while on the GPS, however, especially when you first get it (i.e. the phone has no idea where it is).
