LinuxQuestions.org - Ping: unknown (local) host, FC-12, w/ router & DSL modem, not newbie, but stumped.

Please pardon the length of this plea for help, but I want to lay out all the info I think is relevant.

Three PCs are connected to a Linksys WRT54GL router (no wireless involved here.)
The router is addressed as 192.168.2.1 and provides DHCP to the PCs.

The router is connected to a Westell Verizon DSL modem.
The modem is addressed as 192.168.1.1 and provides DHCP to the router
(192.168.1.45)

All three PCs connect to external internet properly.
The router's DHCP client table shows all three PCs by name with their
assigned address, typically those in the table below.

PROBLEM:
The two FC-12 PCs CANNOT ping the others BY NAME but CAN ping BY ADDRESS.
Also the FC-12 PCs that can ping by address but not by name can also ssh, etc by address, but not by name.

The FC-12 PCs CAN ping external servers such as google.com, yahoo.com, properly.

The W-XP PC, however, CAN ping the FC-12 PCs by name, e.g from "A" I can ping "B" and "C".

BUT:
The FC-12 PCs CAN see the other PCs using the 'network places' Gnome GUI, and CAN copy files among them using drag-and-drop. !!!

ALSO:
Addressing the PCs by name used to work when I had AT&T DSL service, but something changed when the router was configured for Verizon DSL service. Previously, the router was set to PPPOE, and I used static addresses on all PC's, now its set to DHCP, as per Verizon. I removed the static addresses from /etc/hosts on the FC-12 PCs.

Also, from the W-XP side, the FC-12 SMB clients seem to work properly.

Here is the situation:
------------------------------------------------------------------------------------

Code:

PC  OS    typical  DHCP  can ping  can ping  can ping  can ping  can ping  can ping

                IP      ... .110      A    ... .111      B    ... .112    C

==  =====  =============  ========  ========  ========  ======== ========  ========

A  W-XP  192.168.2.110    yes      yes      yes      yes      yes      yes  

B  FC-12  192.168.2.111    yes      no        yes      no      yes      no  

C  FC-12  192.168.2.112    yes      no        yes      no      yes      no

Code:

[B]$ ping 192.168.2.110    {B pinging A by address}

PING 192.168.2.110 (192.168.2.110) 56(84) bytes of data.

64 bytes from 192.168.2.110: icmp_seq=1 ttl=128 time=0.287 ms

64 bytes from 192.168.2.110: icmp_seq=2 ttl=128 time=0.276 ms

64 bytes from 192.168.2.110: icmp_seq=3 ttl=128 time=0.292 ms

^C

--- 192.168.2.110 ping statistics ---

3 packets transmitted, 3 received, 0% packet loss, time 2334ms

rtt min/avg/max/mdev = 0.276/0.285/0.292/0.006 ms



[B]$ ping A                {B pinging A by name}

ping: unknown host A



-----------------------------------------------------------------------------------

[B]$ cat /etc/resolv.conf  { same on C }

; generated by /sbin/dhclient-script

search GAMMA5 

nameserver 192.168.2.1    { the router }

nameserver 192.168.1.1    { the DSL modem }

-----------------------------------------------------------------------------------



From C: { or B }

[C]$ ping -c2 google.com

PING google.com (66.249.81.104) 56(84) bytes of data.

64 bytes from lga15s01-in-f104.1e100.net (66.249.81.104): icmp_seq=1 ttl=47 time=27.8 ms

64 bytes from lga15s01-in-f104.1e100.net (66.249.81.104): icmp_seq=2 ttl=47 time=28.0 ms



--- google.com ping statistics ---

2 packets transmitted, 2 received, 0% packet loss, time 1029ms

rtt min/avg/max/mdev = 27.857/27.955/28.053/0.098 ms

========================================================================
Since the W-XP box can ping the others by name I conclude:
1) nothing is blocking ping protocols.
2) there is a DNS server working in the router (or somewhere else)

What do I have to do in the FC-12 PC's to get name resolution for the other PC's?
Which daemons should be running on the FC-12 boxes?
Which should NOT be running on the FC-12 boxes?
What do I check in iptables etc to make sure this is not the problem?

Thanks for any suggestions to fix this problem.

-Al