vista internet connection

I can log onto the internet fine at home with my own wireless network but
there are some public places(coffee shops) that I am unable to connect with.
The symbol at the bottom shows a local connection but no internet connection.
These are places that I have previously been able to get onto the internet
fine with the same computer and running vista. Has anyone encountered this
problem? I'm not understanding why I'm getting the local connection but no
internet connection the wireless networks do show up and seem to connect
fine. Any help would be apprectiated.

Compaq Presario F557FUS
Vista Basic
Nvidia 6150
1GB memory
2GB ram
Mobile AMD Sempron(tm) Processor 3500+ 1.80 GHz
32-bit operating system