I have a small network consisting of two computers.

One computer runs Mac OS X. The other computer dual boots between Windows XP Professional and Fedora Core 2.

When I'm running Windows both computers are able to ping each other. When I'm running Linux, neither computer can ping the other.

What could be the cause for this?

ethernet card not active (do you have an IP)

start with ifconfig

I believe the ethernet card is working.

The two systems are connected to the Internet via a router. Both systems can ping the router, and both have no problems accessing the Internet.

Does this mean you can ping the router from your Linux box?

Check the firewall rules on your Linux box ... it could be blocking incoming pings.

Yes the Linux system can ping the router.

How do I check the firewall rules?

/sbin/iptables -L

Here are the results I get from checking the firewall rules:

Chain INPUT (policy ACCEPT)
target prot opt source destination
LINWIZ-INPUT all -- anywhere anywhere

Chain FORWARD (policy ACCEPT)
target prot opt source destination

Chain OUTPUT (policy ACCEPT)
target prot opt source destination

Chain ADDRESS-FILTER (1 references)
target prot opt source destination
RETURN all -- Vega.verizon.net anywhere
RETURN all -- tkd.verizon.net anywhere
RETURN all -- 192.168.0.4 anywhere
REJECT-PKT all -- anywhere anywhere

Chain LINWIZ-INPUT (1 references)
target prot opt source destination
ACCEPT all -- anywhere anywhere
DROP all -- 127.0.0.0/8 anywhere
DROP all -- anywhere 127.0.0.0/8
DROP all -- Vega.verizon.net anywhere
SYN-FLOOD tcp -- anywhere anywhere tcp flags:SYN,RST,ACK/SYN
DROP tcp -- anywhere anywhere tcp flags:!SYN,RST,ACK/SYN state NEW
ACCEPT all -- anywhere anywhere state RELATED,ESTABLISHED
ACCEPT icmp -- anywhere anywhere icmp echo-request
ADDRESS-FILTER all -- anywhere anywhere
ACCEPT tcp -- anywhere anywhere tcp dpt:sunrpc
ACCEPT tcp -- anywhere anywhere tcp dpt:nfs
ACCEPT tcp -- anywhere anywhere tcp dpts:4000:4003
ACCEPT udp -- anywhere anywhere udp dpt:sunrpc
ACCEPT udp -- anywhere anywhere udp dpt:nfs
ACCEPT udp -- anywhere anywhere udp dpts:4000:4003
REJECT-PKT all -- anywhere anywhere

Chain REJECT-PKT (2 references)
target prot opt source destination
REJECT tcp -- anywhere anywhere tcp reject-with tcp-reset
REJECT udp -- anywhere anywhere udp reject-with icmp-port-unreachable
REJECT icmp -- anywhere anywhere icmp echo-request reject-with icmp-host-unreachable

Chain SYN-FLOOD (1 references)
target prot opt source destination
RETURN all -- anywhere anywhere limit: avg 1/sec burst 4
DROP all -- anywhere anywhere

#iptables -nvL

would give you a more detailed report.

iptables -L could be confusing as it does not include interface information.

prevents pings from being answered.

This may be important; when I'm booting up I get some [ Failed ] message scroll by that look like they are related to ipchains in character based portion of the boot process. I can never read what the message are because the scroll by too quickly.
Here are the results of running iptables -nvL:

Chain INPUT (policy ACCEPT 0 packets, 0 bytes)
pkts bytes target prot opt in out source destination
10430 625K LINWIZ-INPUT all -- * * 0.0.0.0/0 0.0.0.0/0

Chain FORWARD (policy ACCEPT 0 packets, 0 bytes)
pkts bytes target prot opt in out source destination

Chain OUTPUT (policy ACCEPT 10467 packets, 550K bytes)
pkts bytes target prot opt in out source destination

Chain ADDRESS-FILTER (1 references)
pkts bytes target prot opt in out source destination
0 0 RETURN all -- * * 192.168.0.2 0.0.0.0/0
0 0 RETURN all -- * * 192.168.0.3 0.0.0.0/0
0 0 RETURN all -- * * 192.168.0.4 0.0.0.0/0
9 648 REJECT-PKT all -- * * 0.0.0.0/0 0.0.0.0/0

Chain LINWIZ-INPUT (1 references)
pkts bytes target prot opt in out source destination
10136 513K ACCEPT all -- lo * 0.0.0.0/0 0.0.0.0/0
0 0 DROP all -- * * 127.0.0.0/8 0.0.0.0/0
0 0 DROP all -- * * 0.0.0.0/0 127.0.0.0/8
2 470 DROP all -- * * 192.168.0.2 0.0.0.0/0
0 0 SYN-FLOOD tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp flags:0x16/0x02
0 0 DROP tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp flags:!0x16/0x02 state NEW
283 111K ACCEPT all -- * * 0.0.0.0/0 0.0.0.0/0 state RELATED,ESTABLISHED
0 0 ACCEPT icmp -- * * 0.0.0.0/0 0.0.0.0/0 icmp type 8
9 648 ADDRESS-FILTER all -- * * 0.0.0.0/0 0.0.0.0/0
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp dpt:111
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp dpt:2049
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp dpts:4000:4003
0 0 ACCEPT udp -- * * 0.0.0.0/0 0.0.0.0/0 udp dpt:111
0 0 ACCEPT udp -- * * 0.0.0.0/0 0.0.0.0/0 udp dpt:2049
0 0 ACCEPT udp -- * * 0.0.0.0/0 0.0.0.0/0 udp dpts:4000:4003
0 0 REJECT-PKT all -- * * 0.0.0.0/0 0.0.0.0/0

Chain REJECT-PKT (2 references)
pkts bytes target prot opt in out source destination
0 0 REJECT tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp reject-with tcp-reset
9 648 REJECT udp -- * * 0.0.0.0/0 0.0.0.0/0 udp reject-with icmp-port-unreachable
0 0 REJECT icmp -- * * 0.0.0.0/0 0.0.0.0/0 icmp type 8 reject-with icmp-host-unreachable

Chain SYN-FLOOD (1 references)
pkts bytes target prot opt in out source destination
0 0 RETURN all -- * * 0.0.0.0/0 0.0.0.0/0 limit: avg 1/sec burst 4
0 0 DROP all -- * * 0.0.0.0/0 0.0.0.0/0

you can check /var/log/dmesg, /var/log/boot.log and /var/log/messages for boot errors.

As mentioned in my last post, the above rule is blocking your pings.

I checked all these log file and could not find any mention of the errors related to ipchains I see when the system boot up.

Quoting from your first post
Fedora Core 2 does not install ipchains by default.

As far as I know, I haven't done anything to enable ipchains. One poster suggested that I check my firewall settings using iptable. I thought maybe ipchains was in some way related to iptable.

I can't read everything about the warning that appears on the screen when the setting fails. I was able to get some of the information. The warning says something about the fact that ipchains is incompatible with the kernel I am using, and contains some kind of apology from someone named Paul "Rusty" Russel.

All of this may have nothing to do with this problem.

Regarding ipchains .. Run the command

rpm -q ipchains.

If you get a response like ipchains-n.nn, run

rpm -e ipchains

to remove ipchains.

About the ping problem
Have you resolved it?

I have had some success using some iptables commands to change firewall settings.

After issuing the commands, the Linux system can ping the Macintosh. The Macintosh cannot ping the Linux system.