Router – Which hardware router(s) support directing all web traffic through an external proxy server

Think your DHCP options may be off... From: http://www.wlug.org.nz/WPAD

Add the following to your /etc/dhcpd.conf:

option option-252
"http://wpad.host.co.nz/proxy.pac";

With ISC DHCP v3+, option-# options don't work. You have to do this in the global section of your configuration:

option wpad-url code 252 = text;
(define a new option)

And add this in either the global or appropriate subnet section(s) of your configuration:

option wpad-url
"http://wpad.my.domain.tld/proxy.pac\n"; (use new option)

Also, you will find that auth in transparent mode in squid is not really possible. Some commercial web filters do work around this (indeed I work for SmoothWall, one such filter).

It sounds like you have multiple routers and multiple networks. If the two machines aren't on the same network, it won't work. Since each machine sees the other machine's IP address as inside its local network IP range, it assumes it's on the same network. If it's not, it won't work.

If you have two networks both numbered 192.168.0.0/24, a machine one one network won't be able to reach a machine on the other network. Your ping is reaching a different machine on the same network with the same IP address as the machine you were trying to to reach.

When the wireless system happens to connect to the same network, then it all works.

You can confirm this theory as follows: Ping the default gateway on both machines. Then find the default gateway in the ARP table. See if the MAC addresses are the same. If they're not, that's the issue. They're using different routers.

Update: I like Tony Roth's theory. Maybe you have a web proxy configured that's outside of (or not allowing connections to) the local network.