If I understand you correctly, you are connected to LAN that has router as gateway to internet. Also you had wireless connection to your ADSL router that provided you access to internet. In any of this cases router can cause vista to report this kind of problem.
Question is: are you having trouble connecting to all websites or just few, or you can browse web with no problems but you have problems with some programs accessing internet (Skype, torrent client and similar)?
In any case that “remote firewall from a second computer” can be a router on your LAN. Or not
If you are not familiar with network structure I will explain it: you computer (notebook) is connected to a router that is routing network traffic in LAN. If that router has connection to internet (WAN or similar) than it is also gateway for LAN. All devices in LAN and Internet have numerical IP addresses.
For example:
Your notebook has address: 192.168.0.10
Router has address: 192.168.0.1
If router is also gateway then configuration for your notebooks network connection would be something like this:
IP address: 192.168.0.10
Subnet mask: 255.255.255.0
Default Gateway: 192.168.0.1
Domain server: 192.168.0.1-if router supports
You can find out this settings in Vista by keyboard shortcut WindowsKey+R than type cmd hit enter and you got command prompt. Then type: ipconfig /all + Enter and you get settings for all network cards.
Another command that can help you is tracert. Windowskey+R, cmd, enter, and for example type:
tracert
www.google.com and hit enter
You will get data route from your notebook to google.com internet domain. If this command doesn’t result in something that has google in its name, last address is address of computer or device that is causing trouble for you.