Okay, I know this is not anything new, so bear with me.

I am running RH9 and ATTEMPTING to access the internet through a D-Link router using Adelphia cable ISP.

Since the router receives an IP from the ISP and also distributes IP addresses to the home computer(s) I have the following setup

/etc/sysconfig/network

NETWORK=yes
HOST=router host name
GATEWAY=192.168.0.1

/etc/hosts

127.0.0.1 localhost.localdomain localhost
192.168.0.1 router host name

/etc/sysconfig/ifcfg-eth0

DEVICE=eth0
BOOTPROTO=dhcp
ONBOOT=yes

I can ping the router, I can see the IP assigned to the router by the ISP and I can ping the IP assigned, but that is as far as it goes. Regardless of firewall settings, I can't get outside the IP assigned to the router. What am I doing wrong?

ifconfig -a tells me the router has given the linux box an IP and all is well. Any suggestions will be deeply appreciated.

Can you ping an IP address on the web from you router (ex: www.yahoo.com 68.142.226.44) ?
Note that when having IP problem always use IP rather than hostname to test connectivity (to exclude DNS resolution problem).
If you can ping from the router but not from your linux box, than the problem could be

- The routing table of the router (you should have at least a default route pointing to your ISP and a 192.168.0.0 route pointing to you local interface)

- The NAT/PAT config of the router

Have you check those 2 things?
What do you get from a traceroute to yahoo's address from the linux box?

no I can't ping the yahoo address. the traceroute shows a response from the router (192.168.0.1 and the time it took) then followed by lines containing * * *, which I've been assuming is due to a firewall being too picky.

as far as the route pointing to the ISP, could you be a bit more specific, for I feel this is where I am going wrong?

If from your router you cannot ping yahoo, then that the 1st thing to investigate. If it doesn't work from your router, won't work from you PC.
Normally firewall on DSL router for home user are set to allow everything from inside (local LAN) to outside (Internet). So it shouldn't be blocking you traceroute. Although it would be better to disable the firewall until you can make it works.

Here is a typicall (simplified) routing table:

destination ======= > route
_____________________________
192.168.0.0/24 ======= > local ethernet interface
default (or 0.0.0.0) ======= > the IP of your provider next hop


Can you ping from your router the IP of your ISP router (the one the default router is pointing to)?
If yes, can you do a traceroute from your router to yahoo?
You need this to be working before going more deepely into the NAT/PAT config or the router.

u may also have answered ur own question about the firewall too... try disabling it while u r trying to sort out ur network, u can set it up to allow addys once u r up and running :-)

This is an indication that you don't have no or wrong default gateway (gw) set for your router. The default gw should be the one you got from your ISP, an IP address often ending in 1.

Run the following command on your router and post the results here.