Phew, a bit of information might help as there could be a few answers. No
promises I can answer but it will help someone if you can state:-
How is the main computer, computer 1, connected to the internet and does it
run a firewall or are you using the built in Windows ICS?
What is it's operating system?
If it's running a firewall which one and are you familiar with all it's
settings?
What is the OS on computer 2 and is it connected via computer 1 or are they
both through a router?
Can you give an example of a site that works on both machines and then an
example of a site that only works on computer 1?
It sounds like computer 2 is not always able to get DNS translation so the
above info could provide useful clues. To set this up though the OS needs to
be known because (for example) 98 is very different from 2000 / XP.
Can you remember when you set them up if you put in DNS server IP addresses
manually or if you left settings to "Automatic" or DHCP?
Charlie
